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Robust stability and stabilization of discrete-time nonlinear systems: The LMI approach. (English) Zbl 1022.93034

This is the discrete-time version of a previous paper by the same authors [Math. Probl. Eng. 6, 461-493 (2000; Zbl 0968.93075)]. A linear system with additive nonlinear time-varying state dynamics is considered, and provided the nonlinearity is not too much structured (namely, provided it is bounded by some given positive quadratic function of the state), it is shown that stability can be checked (analysis) or ensured (state-feedback design) via convex optimization over linear matrix inequalities (LMIs).
Stability is ensured with the help of a quadratic Lyapunov function. The main result, Theorem 1, is obtained by applying a standard algebraic trick on convexity of quadratic functions, called the S-procedure or also Finsler’s lemma.
Applications to the stability of interconnected systems composed of linear subsystems with uncertain nonlinear couplings are also described.

MSC:

93D09 Robust stability
93C55 Discrete-time control/observation systems
93B51 Design techniques (robust design, computer-aided design, etc.)
93D30 Lyapunov and storage functions
93B40 Computational methods in systems theory (MSC2010)

Citations:

Zbl 0968.93075

Software:

LMI toolbox
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