The bounded real lemma for discrete time-varying systems with application to robust output feedback

Develops a solution to the discrete-time robust output feedback control problem for linear time-varying (LTV) systems. The solution is developed along the strategy set up in Doyle et al. (1989) and the main ingredient in its derivation is the extension of the well-known bounded real lemma in a (discrete) time-varying context, developed in van der Veen and Verhaegen (1993). This approach contributes to the conceptual simplicity, and hence to the accessibility, of the solution. Apart from that, the authors treat the /spl infin/-horizon case for LTV systems of non-uniform state dimension, and varying input and output dimension. Both situations can easily occur in practice, e.g. in multirate sampled data control systems.<<ETX>>

[1]  I. Postlethwaite,et al.  State-space formulae for discrete-time H∞ optimization , 1989 .

[2]  A. Weeren,et al.  The discrete time Riccati equation related to the H∞ control problem , 1992, 1992 American Control Conference.

[3]  Pramod P. Khargonekar,et al.  On the sensitivity minimization problem for linear time varying periodic systems , 1986 .

[4]  B. Anderson,et al.  A game theoretic approach to H ∞ control for time-varying systems , 1992 .

[5]  Gilead Tadmor,et al.  Worst-case design in the time domain: The maximum principle and the standardH∞ problem , 1990, Math. Control. Signals Syst..

[6]  P. Khargonekar,et al.  State-space solutions to standard H2 and H∞ control problems , 1988, 1988 American Control Conference.

[7]  Franklin Fa-Kun Kuo,et al.  Network analysis and synthesis , 1962 .

[8]  A. Stoorvogel The discrete time H∞ control problem with measurement feedback , 1992 .

[9]  P. Khargonekar,et al.  State-space solutions to standard H/sub 2/ and H/sub infinity / control problems , 1989 .

[10]  Lihua Xie,et al.  On the Discrete-time Bounded Real Lemma with application in the characterization of static state feedback H ∞ controllers , 1992 .

[11]  P. Khargonekar,et al.  H ∞ control of linear time-varying systems: a state-space approach , 1991 .

[12]  Bruce A. Francis,et al.  Uniformly optimal control of linear feedback systems , 1985, Autom..

[13]  A. V. D. Veen Time-varying system theory and computational modeling realization, approximation and factorization , 1993 .

[14]  Tamer Basar,et al.  H∞-Optimal Control and Related , 1991 .

[15]  T. Başar Disturbance attenuation in LTI plants with finite horizon: optimality of nonlinear controllers , 1989 .

[16]  Louis Weinberg,et al.  Network Analysis and Synthesis , 1962 .

[17]  Tryphon T. Georgiou,et al.  A constructive algorithm for sensitivity optimization of Periodic systems , 1987 .

[18]  K. Furuta,et al.  An algebraic approach to discrete-time H∞ control problems , 1990, 1990 American Control Conference.

[19]  Giuseppe de Nicolao On the time-varying Riccati difference equation of optimal filtering , 1992 .

[20]  Patrick Dewilde,et al.  Interpolation for upper triangular operators , 1992 .

[21]  A. Weeren,et al.  The discrete-time Riccati equation related to the H∞ control problem , 1994, IEEE Trans. Autom. Control..

[22]  André C. M. Ran A course in H∞− control theory , 1988 .