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Frequency-domain stability conditions for hybrid systems. (English. Russian original) Zbl 1382.93023

Autom. Remote Control 78, No. 12, 2101-2119 (2017); translation from Avtom. Telemekh. 2017, No. 12, 3-25 (2017).
Summary: A special class of the hybrid systems with switchings of time-invariant linear right-hand sides is considered. A narrower subclass of such systems, that of connected switched linear systems, is specified among them. Necessary and sufficient frequency domain conditions (criteria) for the existence of a common quadratic Lyapunov function providing stability of the switched systems are proposed for them. The specified subclass includes control systems with several nonstationary nonlinearities from the finite sectors that are the matter at issue of the theory of absolute stability. For the connected switched linear systems of a special kind (triangular type systems), separate necessary and separate sufficient existence conditions are obtained for such Lyapunov functions. The interrelations between these conditions are discussed in the example.

MSC:

93C80 Frequency-response methods in control theory
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93C15 Control/observation systems governed by ordinary differential equations
93D30 Lyapunov and storage functions
93C05 Linear systems in control theory
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References:

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