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Discretization schemes for Lyapunov-Krasovskii functionals in time-delay systems. (English) Zbl 1265.93176
Summary: This article gives an overview of discretized Lyapunov functional methods for time-delay systems. Quadratic Lyapunov-Krasovskii functionals are discretized by choosing the kernel to be piecewise linear. As a result, the stability conditions may be written in the form of linear matrix inequalities. Conservatism may be reduced by choosing a finer mesh. Simplification techniques including elimination of variables and using integral inequalities are also discussed. Systems with multiple delays and distributed delays are also treated. Finally, the treatment of uncertainties and input-output performance requirements are discussed.

MSC:
93C55 Discrete-time control/observation systems
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
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