Polynomially parameter-dependent Lyapunov functions for robust H-infinity performance analysis

The computation of robust H-infinity 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 Hα 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.