Computation of lower bounds for the optimal quadratic cost of linear switched systems

This paper deals with the problem of finding a lower bound for the optimal value of a quadratic cost functional for a continuous-time autonomous linear switched system. This bound is computed on the basis of a set of matrices that satisfies some mild assumptions. An admissible set can be derived directly from the piecewise quadratic Lyapunov function used to construct a stabilizing conic switching law, for which both a lower and an upper bound can be obtained. The same results are then extended to the discrete-time domain