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Global stabilization of non-linear discrete-time systems by linear feedback. (English) Zbl 1167.93022

The aim of this paper is to derive explicit sufficient conditions for global exponential stability of a class of non-autonomous, nonlinear discrete-time systems using linear feedback. The stability conditions are derived using so named “freezing” method when considered the system with slowly varied parameters when rate of coefficient matrices change is sufficiently small.
Reviewer’s remark: We really have here the usage of comparison method. This method of proof the stability of control differential or discrete-time equations is described in the book: V. M. Matrosov, Vector Lyapunov functions method: nonlinear analysis of dynamical properties (Russian), Moskva: FIZMATLIT (2000; Zbl 0988.34040).

MSC:

93D15 Stabilization of systems by feedback
93C55 Discrete-time control/observation systems
93C10 Nonlinear systems in control theory

Citations:

Zbl 0988.34040
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