A proof of global attractivity for a class of switching systems using a non-quadratic Lyapunov approach (Q2745699)

The authors consider the switched system NEWLINE\[NEWLINE\dot x+A(t)xNEWLINE\]NEWLINE 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 NEWLINE\[NEWLINE\dot x=A_ix,\;i=i,\dots,m.NEWLINE\]NEWLINE 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.