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Exponential stability of simultaneously triangularizable switched systems with explicit calculation of a common Lyapunov function. (English) Zbl 1171.93368
Summary: A common quadratic Lyapunov function is explicitly calculated for a linear hybrid system described by a family of simultaneously triangularizable matrices. The explicit construction of such a function allows not only obtaining an estimate of the convergence rate of the exponential stability of the switched system under arbitrary switching but also calculating an upper bound for the output during its transient response. Furthermore, the presented result is then extended to the case where the system is affected by parametric uncertainty, providing the corresponding results in terms of the nominal matrices and uncertainty bounds.
MSC:
93D05Lyapunov and other classical stabilities of control systems
93D21Adaptive or robust stabilization
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