Guaranteed cost control of uncertain systems via Lur'e-Postnikov Lyapunov functions

It is known in stability analysis that Lyapunov functions of the Lur'e-Postnikov form may have an advantage over quadratic Lyapunov functions. In this paper, a Lyapunov function of the Lur'e-Postnikov form is used for synthesis of a stabilizing controller for an uncertain system with structured norm-bounded uncertainty. An example is given which shows that a controller stabilizing the system with a Lur'e-Postnikov Lyapunov function may guarantee better performance, as compared to a controller synthesised using a standard quadratic Lyapunov function.