Robust H∞ performance of uncertain system based on Lyapunov functions using non-monotonic terms

This work concerns the problem of robust performance by analyzing the H-infinity norm of one dimensional (1D) uncertain linear time invariant systems with external disturbance (noise) while the uncertainty is described as a polytope. The contribution of this work consists of giving a more general methodology, by combining Lyapunov function with Finsler's lemma technique. The objective is to develop a new sufficient conditions by checking an optimal H-infinity performance of uncertain system using a number of Lyapunov functions with derivative of higher order of the state vector in continuous time (difference of higher order of the state vector in the discrete time), moreover some slack and free matrices to eliminate the product between state matrix and Lyapunov matrices, these conditions in this paper are providing in terms of a set of linear matrix inequalities defined at each vertex. Finally, numerical examples are used to demonstrate the benefits of this proposed methodology.