H-infinity output feedback control for linear discrete time-varying systems via the bounded real lemma

Abstract:
In this paper we develop a solution to the discrete-time H-infinity output feedback control problem for Linear Time-Varying (LTV) systems. The solution is developed along the strategy set up in the DGKF paper and the main ingredient in its derivation is the extension of the well-known bounded real lemma to a (discrete) time-varying context, developed in previous work. This approach contributes to the conceptual simplicity, and hence to the accessibility, of the solution. Apart from that, we treat the infinite-horizon case for LTV system 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. The algorithm that can be derived from the solution presented is then applied to the H-infinity output feedback of a dynamical system changing from one operation point in its operation envelope to another.

Keywords:
Positive real lemma, discrete time-varying system, H-infinity control, Riccati equations.

Click HERE to receive a preliminary version of the paper as a gzipped postscript file (92Kb).
Click HERE for a preliminary version of the paper as a in pdf file (181Kb).
A hard copy of the published paper is available upon request.