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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

x ˙+A(t)x

where A(t) is piecewise constant and takes a finite number of values A i , i=1,,m. The exponential stability of this system is ensured by the existence of a common quadratic Lyapunov function x T Px for all constituent system

x ˙=A i x,i=i,,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:
93D30Scalar and vector Lyapunov functions
93B12Variable structure systems
93D20Asymptotic stability of control systems