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A proof of global attractivity for a class of switching systems using a non-quadratic Lyapunov approach. (English) Zbl 0992.93084

The authors consider the switched system \[ \dot x+A(t)x \] where \(A(t)\) is piecewise constant and takes a finite number of values \(A_i\), \(i=1,\dots,m\). The exponential stability of this system is ensured by the existence of a common quadratic Lyapunov function \(x^TPx\) for all constituent system \[ \dot x=A_ix,\;i=i,\dots,m. \] Some new conditions for the existence of such a function are considered; the known conditions are weakened in the sense that upper triangularization of the \(A_i\) no longer needs to be performed via a common similarity transformation.

MSC:

93D30 Lyapunov and storage functions
93B12 Variable structure systems
93D20 Asymptotic stability in control theory

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