Sampled-data mixed H ∞ and passive control for attitude stabilization and vibration suppression of flexible spacecrafts with input delay

Abstract

This paper deals with the problem of mixed $H_{\infty}$ and passive control for flexible spacecrafts subject to nonuniform sampling and time-varying delay in the input channel. An impulsive observer-based controller is introduced and the resulting closed-loop system is a hybrid system consisting of a continuous time-delay subsystem and an impulsive differential subsystem. As a first result, we derive a generalized bounded real lemma (GBRL), that is, a generalized $H_{\infty}$ performance criterion, for the impulsive differential subsystem by constructing a time-varying Lyapunov functional. Then, on the basis of this GBRL and utilizing the Lyapunov–Krasovskii approach, a sufficient condition is derived to asymptotically stabilize the closed-loop system and simultaneously guarantee a prescribed mixed $H_{\infty}$ and passivity performance index. A design method is proposed for the desired controller, which can be readily constructed by solving a convex optimization problem with linear matrix inequalities (LMIs) constraints. Finally, numerical experiments are provided to support the theoretical results, and comparisons with former approaches are also discussed.

Keywords

Flexible spacecraft input delay nonuniform sampling robust control

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