Robust Control With Missing Measurements and Time Delays

In this technical note, the robust H control problem is investigated for a class of stochastic uncertain discrete time-delay systems with missing measurements. The parameter uncertainties enter into the state matrices, and the missing measurements are described by a binary switching sequence satisfying a conditional probability distribution. The purpose of the problem is to design a full-order dynamic feedback controller such that, for all possible missing observations and admissible parameter uncertainties, the closed-loop system is asymptotically mean-square stable and satisfies the prescribed H performance constraint. Delay-dependent conditions are derived under which the desired solution exists, and the controller parameters are designed by solving a linear matrix inequality (LMI). A numerical example is provided to illustrate the usefulness of the proposed design method.

[1]  Lihua Xie,et al.  Output feedback H∞ control of systems with parameter uncertainty , 1996 .

[2]  E. Boukas,et al.  On Stochastic Stabilization of Discrete‐Time Markovian Jump Systems with Delay in State , 2003 .

[3]  C. Scherer,et al.  Multiobjective output-feedback control via LMI optimization , 1997, IEEE Trans. Autom. Control..

[4]  Daniel W. C. Ho,et al.  Variance-constrained filtering for uncertain stochastic systems with missing measurements , 2003, IEEE Trans. Autom. Control..

[5]  Ian R. Petersen,et al.  Model validation and state estimation for uncertain continuous-time systems with missing discrete-continuous data , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[6]  Huijun Gao,et al.  A delay-dependent approach to robust H∞ filtering for uncertain discrete-time state-delayed systems , 2004, IEEE Trans. Signal Process..

[7]  Biao Huang,et al.  H2 approximation of multiple input/output delay systems , 2004 .

[8]  M. Malek-Zavarei,et al.  Time-Delay Systems: Analysis, Optimization and Applications , 1987 .

[9]  D. Hinrichsen,et al.  H∞-type control for discrete-time stochastic systems , 1999 .

[10]  Fuchun Sun,et al.  Design of reduced-order H∞ filter for Markovian jumping systems with time delay , 2004, IEEE Trans. Circuits Syst. II Express Briefs.

[11]  Lihua Xie,et al.  Robust Kalman Filter Design for Discrete Time-Delay Systems , 2002 .

[12]  Nasser E. Nahi,et al.  Optimal recursive estimation with uncertain observation , 1969, IEEE Trans. Inf. Theory.

[13]  I. Petersen,et al.  Robust Filtering with Missing Data and a Deterministic Description of Noise and Uncertainty , 1996 .

[14]  Fuwen Yang,et al.  Robust finite-horizon filtering for stochastic systems with missing measurements , 2005, IEEE Signal Processing Letters.

[15]  J. Lam,et al.  Non‐fragile guaranteed cost control for uncertain descriptor systems with time‐varying state and input delays , 2005 .

[16]  Huijun Gao,et al.  Delay-dependent output-feedback stabilisation of discrete-time systems with time-varying state delay , 2004 .

[17]  E. Boukas,et al.  Optimal guaranteed cost control of uncertain discrete time-delay systems , 2003 .

[18]  Qiang Ling,et al.  Optimal dropout compensation in networked control systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[19]  Emilia Fridman,et al.  Robust H∞ control of distributed delay systems with application to combustion control , 2001, IEEE Trans. Autom. Control..

[20]  K. Åström.  Introduction to Stochastic Control Theory , 1970 .