L2 gain analysis of piecewise linear systems using sums of squares: A negative result
Jun Xu · 2012
In this paper, we investigate the L2gain problem for piecewise linear (PWL) systems. Unlike the piecewise quadratic Lyapunov function (PQLF) approach, we construct high-order polynomial Lyapunov functions using the theory of sums of squares (SOS) with the aid of Positivstelltz and partition-dependent slack variables. We show that although more freedom is provided by SOS polynomials, the result may not be improved by linear matrix inequality (LMI) approach, i.e., SOS has its limitation in analysis of L2gain problem for PWL systems.