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Discrete-time Linear Systems (discrete-time + linear_system)

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Selected Abstracts

Combining state estimator and disturbance observer in discrete-time sliding mode controller design,

ASIAN JOURNAL OF CONTROL, Issue 5 2008
Jeang-Lin Chang
Abstract In response to a multiple input/multiple output discrete-time linear system with mismatched disturbances, an algorithm capable of performing estimated system states and unknown disturbances is proposed first, and then followed with the design of the controller. Attributed to the fact that both system states and disturbances can be estimated simultaneously with our proposed method, the estimation error is constrained at less than O(T) as the disturbance between the two sampling points is insignificant. In addition, the estimated system states and disturbances are then to be used in the controller when implementing our algorithm in a non-minimum phase system (with respect to the relation between the output and the disturbance). The tracking error is constrained in a small bounded region and the system stability is guaranteed. Finally, a numerical example is presented to demonstrate the applicability of the proposed control scheme. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

On-line almost-sure parameter estimation for partially observed discrete-time linear systems with known noise characteristics

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 6 2002
Robert J. Elliott
Abstract In this paper we discuss parameter estimators for fully and partially observed discrete-time linear stochastic systems (in state-space form) with known noise characteristics. We propose finite-dimensional parameter estimators that are based on estimates of summed functions of the state, rather than of the states themselves. We limit our investigation to estimation of the state transition matrix and the observation matrix. We establish almost-sure convergence results for our proposed parameter estimators using standard martingale convergence results, the Kronecker lemma and an ordinary differential equation approach. We also provide simulation studies which illustrate the performance of these estimators. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Active mode observation of switching systems based on set-valued estimation of the continuous state

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 14 2009
M. Baglietto
Abstract Mode observability is addressed for a class of discrete-time linear systems that may switch in an unknown and unpredictable way among different modes taken from a finite set. The possible a priori knowledge on the continuous state of the system and the presence of unknown but bounded noises affecting both the system and the measurement equations are explicitly taken into account. The mode observation is performed ,actively': control sequences (discerning control sequences) are searched, which allow to identify the switching sequence on the basis of the observations. Conditions that characterize discerning controls in a finite-horizon setting are obtained. Moreover, a procedure is proposed in order to derive ,persistently discerning' control sequences (over an infinite horizon). A numerical example is reported to clarify the approach. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Observer design with guaranteed RMS gain for discrete-time LPV systems with Markovian jumps

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 6 2009
Giuseppe C. Calafiore
Abstract In this paper we consider the problem of designing state observers with guaranteed power-to-power (RMS) gain for a class of stochastic discrete-time linear systems that possess both measurable parameter variations and Markovian jumps in their dynamics. It is shown in the paper that an upper bound on the RMS gain of the observer can be characterized in terms of feasibility of a family of parameter-dependent linear matrix inequalities (LMIs). Any feasible solution to these LMIs can then be used to explicitly construct a parameter-varying jump observer that guarantees the desired performance level. This design framework is then specialized to a problem of state estimation for a linear parameter-varying plant whose state measurements are available through a lossy Bernoulli channel. Two numerical examples illustrate the results. Copyright © 2008 John Wiley & Sons, Ltd. [source]

On the componentwise stability of linear systems

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 1 2005
O. Pastravanu
Abstract The componentwise asymptotic stability (CWAS) and componentwise exponential asymptotic stability (CWEAS) represent stronger types of asymptotic stability, which were first defined for symmetrical bounds constraining the flow of the state-space trajectories, and then, were generalized for arbitrary bounds, not necessarily symmetrical. Our paper explores the links between the symmetrical and the general case, proving that the former contains all the information requested by the characterization of the CWAS/CWEAS as qualitative properties. Complementary to the previous approaches to CWAS/CWEAS that were based on the construction of special operators, we incorporate the flow-invariance condition into the classical framework of stability analysis. Consequently, we show that the componentwise stability can be investigated by using the operator defining the system dynamics, as well as the standard ,,, formalism. Although this paper explicitly refers only to continuous-time linear systems, the key elements of our work also apply, mutatis mutandis, to discrete-time linear systems. Copyright © 2004 John Wiley & Sons, Ltd. [source]

,, filtering for discrete-time linear systems with Markovian jumping parameters,,

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 14 2003
Carlos E. de Souza
Abstract This paper investigates the problem of ,, filtering for discrete-time linear systems with Markovian jumping parameters. It is assumed that the jumping parameter is available. This paper develops necessary and sufficient conditions for designing a discrete-time Markovian jump linear filter which ensures a prescribed bound on the ,2 -induced gain from the noise signals to the estimation error. The proposed filter design is given in terms of linear matrix inequalities. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Robust Kalman filtering for uncertain discrete-time linear systems

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 13 2003
Germain Garcia
Abstract This paper presents a steady-state robust state estimator for a class of uncertain discrete-time linear systems with norm-bounded uncertainty. It is shown that if the system satisfies some particular structural conditions and if the uncertainty has a specific structure, the gain of the robust estimator (which assures a guaranteed cost) can be calculated using a formula only involving the original system matrices. Among the conditions the system has to satisfy, the strongest one relies on a minimum phase argument. It is also shown that under the assumptions considered, the robust estimator is in fact the Kalman filter for the nominal system. Copyright © 2003 John Wiley & Sons, Ltd. [source]

,, control of discrete-time Markov jump systems with bounded transition probabilities

OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 5 2009
E. K. Boukas
Abstract This paper deals with the class of discrete-time linear systems with random abrupt changes and unknown transition probabilities but varying between known bounds for each mode. The ,, control problem of this class of systems is revisited and new sufficient conditions are developed in the linear matrix inequality (LMI) setting to design the state-feedback controller that stochastically stabilizes the system under consideration and at the same time guarantees the disturbance rejection with a desired level , . Sufficient conditions for existence of the state-feedback controller are developed. It is shown that the addressed problem can be solved if the corresponding developed LMIs are feasible. Numerical examples are employed to show the usefulness of the proposed results. Copyright © 2008 John Wiley & Sons, Ltd. [source]

On stability and stabilizability of positive delay systems,

ASIAN JOURNAL OF CONTROL, Issue 2 2009
Ligang Wu
Abstract The stabilization problem with positivity is investigated in this note for discrete-time linear systems with time delay. A delay-independent necessary and sufficient condition is proposed in terms of linear matrix inequalities (LMIs) for the existence of desired controllers that guarantee the closed-loop system to be asymptotically stable and positive. In addition, the obtained result is further extended to more general case when the system matrices contain uncertain parameters, where a sufficient condition is obtained. The frequently used polytopic parameter uncertainty is taken into consideration. Since the conditions obtained are expressed as LMIs, which can be easily verified by using standard numerical software. A numerical example is provided to illustrate the proposed results. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

STOCHASTIC STABILIZATION AND H, CONTROL FOR DISCRETE JUMPING SYSTEMS WITH TIME DELAYS

ASIAN JOURNAL OF CONTROL, Issue 3 2005
Jing Wu
ABSTRACT In this paper, robust stochastic stabilization and H, control for a class of uncertain discrete-time linear systems with Markovian jumping parameters are considered. Based on a new bounded real lemma derived upon an inequality recently proposed, a new iterative state-feedback controller design procedure for discrete time-delay systems is presented. Sufficient conditions for stochastic stabilization are derived in the form of linear matrix inequalities (LMIs) based on an equivalent model transformation, and the corresponding H, control law is given. Finally, numerical examples are given to illustrate the solvability of the problems and effectiveness of the results. [source]

Robust Analysis of Discrete-Time Lur'e Systems with Slope Restrictions Using Convex Optimization

ASIAN JOURNAL OF CONTROL, Issue 2 2002
David Banjerdpongchai
ABSTRACT This paper considers robust stability and robust performance analysis for discrete-time linear systems subject to nonlinear uncertainty. The uncertainty set is described by memoryless, time-invariant, sector bounded, and slope restricted nonlinearities. We first give an overview of the absolute stability criterion based on the Lur'e-Postkinov Lyapunov function, along with a frequency domain condition. Subsequently, we derive sufficient conditions to compute the upper bounds of the worst case H2 and worst case H, performance. For both robust stability testing and robust performance computation, we show that these sufficient conditions can be readily and efficiently determined by performing convex optimization over linear matrix inequalities. [source]