On the Peak of the Impulse Response of Polytopic LTV Systems

This paper addresses the problem of determining the peak of the impulse response of polytopic linear time-varying (LTV) systems. In particular, linear systems affected linearly by time-varying structured uncertainty constrained into a polytope are considered. 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). The proposed condition is sufficient for any degree of a polynomial introduced to describe the impulse response, moreover, its conservatism can be decreased by increasing this degree. Some examples illustrate the use of the proposed condition and show the application to a DC motor with time-varying uncertain parameters.