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Stability and optimal control of nonlinear descriptor systems: A survey. (English) Zbl 0910.93047

A survey of recent results on the stability analysis and on the optimal control of nonlinear descriptor systems is presented. The stability analysis is based on Lyapunov’s stability theory with respect to a part of the variables. The notion of causality for nonlinear descriptor systems is introduced. It is shown that for causal systems the calculus of variations and Pontryagin’s maximum principle can be used.

MSC:

93C35 Multivariable systems, multidimensional control systems
93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
93D20 Asymptotic stability in control theory
49N10 Linear-quadratic optimal control problems
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