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Linear Discrete-time Systems (linear + 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]

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]

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]

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]

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 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]