Parameter-dependent Lyapunov functions for state-derivative feedback control in polytopic linear systems

Abstract

In some practical problems, for instance, the suppression of vibration in mechanical systems, the state-derivative signals are easier to obtain than the state signals. Using Linear Matrix Inequalities (LMIs), and applying the reciprocal projection lemma in a Parameter-dependent Lyapunov Function (PDLF), this article proposes a method for the design of state-derivative feedback applied to uncertain linear systems. The control design aims the system stabilisation without and with decay rate restriction. When considering only the system stability, the proposed methodology becomes practically equivalent to the Common Quadratic Lyapunov Function (CQLF) technique. Otherwise, when the decay rate is taken in account, the proposed methodology is shown to be less conservative. Numerical examples illustrate its efficiency.