Tools for Semiglobal Practical Stability Analysis of Cascaded Systems and Applications

Antoine Chaillet

Université Paris Sud – LSS, Supélec, 3 rue Joliot Curie, 91192 - Gif sur Yvette, France

ABSTRACT. We present sufficient conditions for semiglobal and/or practical stability in terms of Lyapunov-like functions. Based on this, we provide a result for the stability analysis of cascaded systems. A converse result is also presented for a particular class of uniformly semiglobally practically asymptotically stable systems. We briefly show the usefulness of these results through various applications in the control of mechanical systems.

KEYWORDS: Lyapunov stability analysis, nonlinear time-varying systems, cascades, semiglobal practical stability

1. Introduction

Cascaded dynamical systems appear in many control applications whether naturally or intentionally due to control design. Cascades-based control consists in designing the control law so that the closed-loop system has a cascaded structure (see e.g. [KRS 95, LEF 00, LOR 04]). From a theoretical viewpoint, the problem of stability analysis of cascaded systems has attracted the interest of the community since the seminal paper [SUS 91], see also [SEP 97] and references therein. A fundamental result states that the cascade of uniformly globally asymptotically stable (UGAS) systems remains UGAS if and only if its solutions are uniformly globally bounded. This has been proved in [SEI 90, SON 89] in ...

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