On the computation of the peak of the impulse response of LTI systems

Abstract

This paper addresses the problem of determining the peak of the impulse response of continuous-time linear time-invariant (LTI) systems, a classical problem in systems theory. A novel condition for establishing upper bounds of the sought peak is proposed in terms of feasibility of a system of linear matrix inequalities (LMIs). This condition is obtained by describing the trajectory of the system through the level set of a polynomial, by using projection techniques for evaluating the position of the level set, and by exploiting the Gram matrix method. The proposed condition is sufficient for any degree of the polynomial, moreover, the conservatism can be decreased by increasing this degree. As shown by some examples, the proposed condition provides significantly less conservative results than the existing methods.