Polynomially Parameter-dependent Lyapunov Functions for Robust H∞ Performance Analysis

The computation of robust H∞ performance of linear systems subject to polytopic parametric uncertainty is known to be a difficult problem in robust control. In this paper, quadratic parameter-dependent Lyapunov functions, with polynomial dependence on the uncertain parameters, are exploited to provide upper bounds to the robust H∞ performance. It is shown that such bounds can be computed via convex optimizations constrained by LMIs. Numerical examples show that the proposed technique is a powerful alternative to existing methods based on linearly parameter-dependent Lyapunov functions. Copyright c ©2005 IFAC