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Discrete-time Systems (discrete-time + system)

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Engineering100%

Kinds of Discrete-time Systems

  • linear discrete-time system
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  • nonlinear discrete-time system
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    Selected Abstracts

    Necessary and sufficient conditions for solving consensus problems of double-integrator dynamics via sampled control

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 15 2010
    Huiyang Liu
    Abstract In this paper, consensus problems of double-integrator dynamics via sampled control are investigated. The sampled control protocol is induced from continuous-time linear consensus protocol by using periodic sampling technology and zero-order hold circuit. With the obtained sampled control protocol, the continuous-time multi-agent system is equivalently transformed into a linear discrete-time system. Necessary and sufficient conditions are given to guarantee that all the agents asymptotically travel with zero relative positions and common velocities. Furthermore, consensus problem with continuous-time consensus protocol is re-analyzed. A necessary and sufficient condition is also obtained which is consistent with the special case when the sampling period tends to zero. The effectiveness of these algorithms is demonstrated through simulations. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    Delay-dependent robust control for singular discrete-time Markovian jump systems with time-varying delay

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 10 2010
    Wuneng Zhou
    Abstract The problem of delay-dependent robust stabilization for uncertain singular discrete-time systems with Markovian jumping parameters and time-varying delay is investigated. In terms of free-weighting-matrix approach and linear matrix inequalities, a delay-dependent condition is presented to ensure a singular discrete-time system to be regular, causal and stochastically stable based on which the stability analysis and robust stabilization problem are studied. An explicit expression for the desired state-feedback controller is also given. Some numerical examples are provided to demonstrate the effectiveness of the proposed approach. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    H2 -OPTIMAL SAMPLED-DATA CONTROL FOR PLANTS WITH MULTIPLE INPUT AND OUTPUT DELAYS

    ASIAN JOURNAL OF CONTROL, Issue 2 2006
    Konstantin Yu.
    ABSTRACT The sampled-data H2 -optimization problem for plants with multiple input and output delays is considered. An equivalent discrete-time system is constructed and numerical algorithm for computing matrices of its state-space realization is presented. It is proved that stability of this system is equivalent to stability of original sampled-data system. The proposed method can be applied to a wide class of digital control problems for continuous-time plants with multiple input and output delays. [source]

    A subspace algorithm for simultaneous identification and input reconstruction

    INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 12 2009
    Harish J. Palanthandalam-Madapusi
    Abstract This paper considers the concept of input and state observability, that is, conditions under which both the unknown input and initial state of a known model can be determined from output measurements. We provide necessary and sufficient conditions for input and state observability in discrete-time systems. Next, we develop a subspace identification algorithm that identifies the state-space matrices and reconstructs the unknown input using output measurements and known inputs. Finally, we present several illustrative examples, including a nonlinear system in which the unknown input is due to the endogenous nonlinearity. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Improved adaptive control for the discrete-time parametric-strict-feedback form

    INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 12 2009
    Graciela Adriana González
    Abstract Adaptive control design for a class of single-input single-output nonlinear discrete-time systems in parametric-strict-feedback form is re-visited. No growth restrictions are assumed on the nonlinearities. The control objective is to achieve tracking of a reference signal. As usual, the algorithm derives from the combination of a control law and a parameter estimator (certainty equivalence principle). The parameter estimator strongly lies on the regressor subspace identification by means of an orthogonalization process. Certain drawbacks of previous schemes are analyzed. Several modifications on them are considered to improve the algorithm complexity, control performance and numerical stability. As a result, an alternative control scheme is proposed. When applied to the proposed class of systems, global boundedness and convergence remain as achieved objectives while improving the performance issues of previous schemes. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    Robust H, filtering for switched linear discrete-time systems with polytopic uncertainties

    INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 6 2006
    Lixian Zhang
    Abstract In this paper, the problem of robust H, filtering for switched linear discrete-time systems with polytopic uncertainties is investigated. Based on the mode-switching idea and parameter-dependent stability result, a robust switched linear filter is designed such that the corresponding filtering error system achieves robust asymptotic stability and guarantees a prescribed H, performance index for all admissible uncertainties. The existence condition of such filter is derived and formulated in terms of a set of linear matrix inequalities (LMIs) by the introduction of slack variables to eliminate the cross coupling of system matrices and Lyapunov matrices among different subsystems. The desired filter can be constructed by solving the corresponding convex optimization problem, which also provides an optimal H, noise-attenuation level bound for the resultant filtering error system. A numerical example is given to show the effectiveness and the potential of the proposed techniques. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    Robust adaptive tracking control of uncertain discrete time systems

    INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 9 2005
    Shengping Li
    Abstract In this paper, the problem of robust adaptive tracking for uncertain discrete-time systems is considered from the slowly varying systems point of view. The class of uncertain discrete-time systems considered is subjected to both ,,, to ,,, bounded unstructured uncertainty and external additive bounded disturbances. A priori knowledge of the dynamic model of the reference signal to be tracked is not completely known. For such problem, an indirect adaptive tracking controller is obtained by frozen-time controllers that at each time optimally robustly stabilize the estimated models of the plant and minimize the worst-case steady-state absolute value of the tracking error of the estimated model over the model uncertainty. Based on ,,, to ,,, stability and performance of slowly varying system found in the literature, the proposed adaptive tracking scheme is shown to have good robust stability. Moreover, a computable upper bound on the size of the unstructured uncertainty permitted by the adaptive system and a computable tight upper bound on asymptotic robust steady-state tracking performance are provided. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    On the existence of common quadratic Lyapunov functions for second-order linear time-invariant discrete-time systems

    INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 10 2002
    Mehmet Akar
    Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function (CQLF) are given for two second-order linear time-invariant discrete-time systems. These conditions are later extended to an arbitrary number of systems. The conditions are readily verifiable both analytically and graphically. The paper also provides a constructive procedure for computing a CQLF when it exists. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Stability and linearization: discrete-time systems

    INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 5 2002
    Irwin W. Sandberg
    Abstract A theorem by Hadamard gives a two-part condition under which a map from one Banach space to another is a homeomorphism. The theorem, while often very useful, is incomplete in the sense that it does not explicitly specify the family of maps for which the condition is met. Recently, under a typically weak additional assumption on the map, it was shown that Hadamard's condition is met if and only if the map is a homeomorphism with a Lipschitz continuous inverse. Here an application is given concerning the relation between the stability of a discrete-time non-linear system and the stability of related linear systems. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Semi-global stabilization of discrete-time systems subject to non-right invertible constraints

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 11 2010
    Xu Wang
    Abstract This paper investigates time-invariant linear systems subject to input and state constraints. We study discrete-time systems with full or partial constraints on both input and state. It has been shown earlier that the solvability conditions of stabilization problems are closely related to important concepts such as the right invertibility or non-right invertibility of the constraints, the location of constraint invariant zeros, and the order of constraint infinite zeros. In this paper, for general time-invariant linear systems with non-right invertible constraints, necessary and sufficient conditions are developed under which semi-global stabilization in the admissible set can be achieved by state feedback. Sufficient conditions are also developed for such a stabilization in the case where measurement feedback is used. Such sufficient conditions are almost necessary. Controllers for both state feedback and measurement feedback are constructed as well. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    Delay-dependent robust control for singular discrete-time Markovian jump systems with time-varying delay

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 10 2010
    Wuneng Zhou
    Abstract The problem of delay-dependent robust stabilization for uncertain singular discrete-time systems with Markovian jumping parameters and time-varying delay is investigated. In terms of free-weighting-matrix approach and linear matrix inequalities, a delay-dependent condition is presented to ensure a singular discrete-time system to be regular, causal and stochastically stable based on which the stability analysis and robust stabilization problem are studied. An explicit expression for the desired state-feedback controller is also given. Some numerical examples are provided to demonstrate the effectiveness of the proposed approach. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    Observer design for nonlinear discrete-time systems: Immersion and dynamic observer error linearization techniques

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 5 2010
    Jian Zhang
    Abstract This paper focuses on the observer design for nonlinear discrete-time systems by means of nonlinear observer canonical form. At first, sufficient and necessary conditions are obtained for a class of autonomous nonlinear discrete-time systems to be immersible into higher dimensional observer canonical form. Then a method called dynamic observer error linearization is developed. By introducing a dynamic auxiliary system, the augmented system is shown to be locally equivalent to the generalized observer form, whose nonlinear terms contain auxiliary states and output of the system. A constructive algorithm is also provided to obtain the state coordinate transformation. These results are an extension of their counterparts of nonlinear continuous-time systems to nonlinear discrete-time systems (Syst. Control Lett. 1986; 7:133,142; SIAM. J. Control Optim. 2003; 41:1756,1778; Int. J. Control 2004; 77:723,734; Automatica 2006; 42:321,328; IEEE Trans. Automat. Control 2007; 52:83,88; IEEE Trans. Automat. Control 2004; 49:1746,1750; Automatica 2006; 42:2195,2200; IEEE Trans. Automat. Control 1996; 41:598,603; Syst. Control Lett. 1997; 31:115,128). Copyright © 2009 John Wiley & Sons, Ltd. [source]

    Linear quadratic regulation for systems with time-varying delay

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 3 2010
    Huanshui Zhang
    Abstract In this paper we study the linear quadratic regulation (LQR) problem for discrete-time systems with time-varying delay in the control input channel. We assume that the time-varying delay is of a known upper bound, then the LQR problem is transformed into the optimal control problem for systems with multiple input channels, each of which has single constant delay. The optimal controller is derived by establishing a duality between the LQR and a smoothing estimation for an associated system with a multiple delayed measurement. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    Stability radii of positive linear systems under fractional perturbations

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 11 2009
    Bui The Anh
    Abstract In this paper we study stability radii of positive linear discrete-time systems under fractional perturbations. It is shown that real and complex stability radii coincide and can be computed by a simple formula. From the obtained results, we apply to derive estimates and computable formulae for the stability radii of positive linear delay systems. Finally, a simple example is given to illustrate the obtained results. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    LMI approach to reliable guaranteed cost control with multiple criteria constraints: The actuator faults case

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 8 2009
    Dengfeng Zhang
    Abstract Based on the multi-objective optimization strategy and linear matrix inequality approach, the problem of reliable guaranteed cost control with multiple criteria constraints is investigated for a class of uncertain discrete-time systems subject to actuator faults. A fault model in actuators, which considers outage or partial degradation in independent actuators, is adopted. The quadratic stability is proved to be independent of the disturbance and the upper bound of a quadratic cost index is improved. The reliable feedback controller is designed to minimize the upper bound of the quadratic cost index, place all the closed-loop poles in a specified disk, constrain the H, norm level of the disturbance attenuation into a given range and guarantee the magnitudes of control inputs less than the given bound, as well. Thus, the resulting closed-loop system can provide satisfactory stability, transient behavior, disturbance rejection level and optimized upper bound of the quadratic cost performance despite possible actuator faults. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    A predictive control strategy for norm-bounded LPV discrete-time systems with bounded rates of parameter change

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 7 2008
    Alessandro Casavola
    Abstract A novel predictive control strategy for input-saturated norm-bounded linear parameter varying discrete-time systems is proposed. The solution is computed by minimizing an upper bound to the ,worst-case' infinite horizon quadratic cost under the constraint of steering the future state evolutions, emanating from the current state, into a feasible and positive invariant set. It will be shown that the ,size' of this terminal set depends on the rate of change of the scheduling parameter, which is assumed to be bounded and measurable. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    A new finite sum inequality approach to delay-dependent H, control of discrete-time systems with time-varying delay

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 6 2008
    Xian-Ming Zhang
    Abstract This paper deals with delay-dependent H, control for discrete-time systems with time-varying delay. A new finite sum inequality is first established to derive a delay-dependent condition, under which the resulting closed-loop system via a state feedback is asymptotically stable with a prescribed H, noise attenuation level. Then, an iterative algorithm involving convex optimization is proposed to obtain a suboptimal H, controller. Finally, two numerical examples are given to show the effectiveness of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    A nonlinear minimization approach to multiobjective and structured controls for discrete-time systems

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 16 2004
    Kwan Ho Lee
    Abstract In this paper, a nonlinear minimization approach is proposed for multiobjective and structured controls for discrete-time systems. The problem of finding multiobjective and structured controls for discrete-time systems is represented as a quadratic matrix inequality problem. It is shown that the problem is reduced to a nonlinear minimization problem that has a concave objective function and linear matrix inequality constraints. An algorithm for the nonlinear minimization problem is proposed, which is easily implemented with existing semidefinite programming algorithms. The validity of the proposed algorithm is illustrated by comparisons with existing methods. In addition, applications of this work are demonstrated via numerical examples. Copyright © 2004 John Wiley & Sons, Ltd. [source]

    Inverse filtering and deconvolution

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 2 2001
    Ali Saberi
    Abstract This paper studies the so-called inverse filtering and deconvolution problem from different angles. To start with, both exact and almost deconvolution problems are formulated, and the necessary and sufficient conditions for their solvability are investigated. Exact and almost deconvolution problems seek filters that can estimate the unknown inputs of the given plant or system either exactly or almostly whatever may be the unintended or disturbance inputs such as measurement noise, external disturbances, and model uncertainties that act on the system. As such they require strong solvability conditions. To alleviate this, several optimal and suboptimal deconvolution problems are formulated and studied. These problems seek filters that can estimate the unknown inputs of the given system either exactly, almostly or optimally in the absence of unintended (disturbance) inputs, and on the other hand, in the presence of unintended (disturbance) inputs, they seek that the influence of such disturbances on the estimation error be as small as possible in a certain norm (H2 or H,) sense. Both continuous- and discrete-time systems are considered. For discrete-time systems, the counter parts of all the above problems when an ,,-step delay in estimation is present are introduced and studied. Next, we focus on the exact and almost deconvolution but this time when the uncertainties in plant dynamics can be structurally modeled by a ,-block as a feedback element to the nominally known plant dynamics. This is done either in the presence or absence of external disturbances. Copyright © 2001 John Wiley & Sons, Ltd. [source]

    Controller design for optimal tracking response in discrete-time systems

    OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 5 2007
    O. A. Sebakhy
    Abstract The problem of designing a controller, which results in a closed-loop system response with optimal time-domain characteristics, is considered. In the approach presented in this paper, the controller order is fixed (higher than pole-placement order) and we seek a controller that results in closed-loop poles at certain desired and pre-specified locations; while at the same time the output tracks the reference input in an optimal way. The optimality is measured by requiring certain norms on the error sequence,between the reference and output signals,to be minimum. Several norms are used. First, l2 -norm is used and the optimal solution is computed in one step of calculations. Second, l, -norm (i.e. minimal overshot) is considered and the solution is obtained by solving a constrained affine minimax optimization problem. Third, the l1 -norm (which corresponds to the integral absolute error-(IAE)-criterion) is used and linear programming techniques are utilized to solve the problem. The important case of finite settling time (i.e. deadbeat response) is studied as a special case. Examples that illustrate the different design algorithms and demonstrate their feasibility are presented. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    H, control of switched linear discrete-time systems with polytopic uncertainties

    OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 5 2006
    Lixian Zhang
    Abstract In this paper, the problem of designing H, state-feedback controllers for switched linear discrete-time systems with polytopic uncertainties is investigated. Two approaches on designing robust and parameter-dependent H, controllers are proposed and the existence conditions of the desired controllers are derived and formulated in terms of a set of linear matrix inequalities. By solving the corresponding convex optimization problem, the desired controllers are obtained, respectively, and different optimal H, noise-attenuation level bounds of corresponding closed-loop systems are given as well. The designed controllers have their own advantages and disadvantages regarding the conservatism and realization complexity. An illustrative example emerging in networked control systems (NCS) and numerical simulations are presented to show the applicability and effectiveness of the obtained theoretic results. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    Unified approach for Euler,Lagrange equation arising in calculus of variations

    OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 6 2004
    D. S. Naidu
    Abstract We address the development of a unified approach for the necessary conditions for optimization of a functional arising in calculus of variations. In particular, we develop a unified approach for the Euler,Lagrange equation, that is simultaneously applicable to both shift (q)-operator-based discrete-time systems and the derivative (d/dt)-operator-based continuous-time systems. It is shown that the Euler,Lagrange results that are now obtained separately for continuous- and discrete-time systems can be easily obtained from the unified approach. An illustrative example is given. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    Robust disturbance attenuation for discrete-time active fault tolerant control systems with uncertainties

    OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 2 2003
    Peng Shi
    Abstract The problems of stochastic stability and stochastic disturbance attenuation for a class of linear discrete-time systems are considered in this paper. The system under study is a state space model possessing two Markovian jump parameters: one is failure process and another is failure detection and isolation scheme. A controller is designed to guarantee the stochastic stability and a disturbance attenuation level. Robustness problems for the above system with norm-bounded parameter uncertainties are also investigated. It is shown that the uncertain system can be robustly stochastically stabilized and have a robust disturbance attenuation level for all admissible perturbations if a set of coupled Riccati inequalities has solutions. A numerical example is given to show the potential of the proposed technique. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    Reduced-order state estimation for linear time-varying systems,

    ASIAN JOURNAL OF CONTROL, Issue 6 2009
    In Sung Kim
    Abstract We consider reduced-order and subspace state estimators for linear discrete-time systems with possibly time-varying dynamics. The reduced-order and subspace estimators are obtained using a finite-horizon minimization approach, and thus do not require the solution of algebraic Lyapunov or Riccati equations. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

    Robust H, control for uncertain discrete-time systems with probabilistic state delays,

    ASIAN JOURNAL OF CONTROL, Issue 5 2009
    Engang Tian
    Abstract In this paper, we propose a novel design problem of robust H, control for discrete-time systems with probabilistic time delay, where both the variation range of the delay and the probability distribution of the delay taking values in an interval are available. Based on the information on the probability distribution of the delay taking values in an interval, a new modeling method is put forward, with which the probabilistic effects of the delay are reflected into a parameter matrix of certain transformed system. Based on such a new model, criteria for the H, control design are derived by using a combination of the convexity of the matrix equations, the Lyapunov functional method and the linear matrix inequality technique. It is shown via numerical examples that our developed method in the paper can lead to less conservative results than those obtained by existing methods and, furthermore, if the probability distribution of the delay occurrence is available, the allowable upper bound of the delay may be larger than those derived for the case when only the variation range of the delay can be known. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

    On ,, model reduction for discrete-time linear time-invariant systems using linear matrix inequalities,

    ASIAN JOURNAL OF CONTROL, Issue 3 2008
    Yoshio Ebihara
    Abstract In this paper, we address the ,, model reduction problem for linear time-invariant discrete-time systems. We revisit this problem by means of linear matrix inequality (LMI) approaches and first show a concise proof for the well-known lower bounds on the approximation error, which is given in terms of the Hankel singular values of the system to be reduced. In addition, when we reduce the system order by the multiplicity of the smallest Hankel singular value, we show that the ,, optimal reduced-order model can readily be constructed via LMI optimization. These results can be regarded as complete counterparts of those recently obtained in the continuous-time system setting. [source]

    ROBUST OUTPUT FEEDBACK CONTROLLER DESIGN WITH COVARIANCE AND DISC CLOSED-LOOP POLE CONSTRAINTS

    ASIAN JOURNAL OF CONTROL, Issue 3 2005
    Li Yu
    ABSTRACT This paper is concerned with the problem of robust output feedback controller design for a class of linear discrete-time systems with normbounded uncertainty. The objective is to design a controller such that the closed-loop poles are assigned within a specified disc and the steady regulated output covariance is guaranteed to be less than a given upper bound. Using a linear matrix inequality (LMI) approach, the existence conditions of such controllers are derived, and a parametrized characterization of a set of desired controllers (if they exist) is presented in terms of the feasible solutions to a set of LMIs. A procedure is given to select a suitable output feedback controller that minimizes the desired control effort. [source]

    LMI APPROACH TO ROBUST FILTERING FOR DISCRETE TIME-DELAY SYSTEMS WITH NONLINEAR DISTURBANCES

    ASIAN JOURNAL OF CONTROL, Issue 2 2005
    Huijun Gao
    ABSTRACT This paper investigates the problem of robust filtering for a class of uncertain nonlinear discrete-time systems with multiple state delays. It is assumed that the parameter uncertainties appearing in all the system matrices reside in a polytope, and that the nonlinearities entering into both the state and measurement equations satisfy global Lipschitz conditions. Attention is focused on the design of robust full-order and reduced-order filters guaranteeing a prescribed noise attenuation level in an H, or l2 - l, sense with respect to all energy-bounded noise disturbances for all admissible uncertainties and time delays. Both delay-dependent and independent approaches are developed by using linear matrix inequality (LMI) techniques, which are applicable to systems either with or without a priori information on the size of delays. [source]