ROBUST STABILITY OF LINEAR TIME-VARYING POLYTOPIC SYSTEMS THROUGH POLYNOMIALLY PARAMETER-DEPENDENT LYAPUNOV FUNCTIONS

This paper addresses the robust stability of linear continuous-time systems affected by uncertain time-varying parameters which belong to a polytope and have bounded rates of variation. The proposed conditions rely on homogeneous polynomially parameter-dependent Lyapunov functions of arbitrary degree, being written as a set of linear matrix inequalities at the vertices of the polytope of uncertainties, taking into account the bounds on the time-derivatives of the uncertain parameters and the degree of the Lyapunov function. Progressively less conservative results can be obtained when the degree of the Lyapunov function is increased, as shown by numerical examples which also illustrate that the proposed conditions yield, with lower computational effort, better results than those from similar tests in the literature.