Stability and control of nonlinear systems described by retarded functional equations: a review of recent results. (English) Zbl 1182.93105
Summary: This paper reports on recent results in a series of the work of the authors on the stability and nonlinear control for general dynamical systems described by retarded functional differential and difference equations. Both internal and external stability properties are studied. The corresponding Lyapunov and Razuminkhin characterizations for input-to-state and input-to-output stabilities are proposed. Necessary and sufficient Lyapunov-like conditions are derived for robust nonlinear stabilization. In particular, an explicit controller design procedure is developed for a new class of nonlinear time-delay systems. Lastly, sufficient assumptions, including a small-gain condition, are presented for guaranteeing the input-to-output stability of coupled systems comprised of retarded functional differential and difference equations.
MSC:
| 93D21 | Adaptive or robust stabilization |
| 93D25 | Input-output approaches in control theory |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
| 93C10 | Nonlinear systems in control theory |
Keywords:
stability; nonlinear control; retarded functional equations; Lyapunov functions; Lyapunov functionalsReferences:
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