On feedback capability of uncertain semiparametric systems

In this paper, we consider discrete-time semiparametric control systems where both parametric and nonparametric uncertainties are included. In particular, we will study the capability of feedback with an unknown parameter in the input channel and will demonstrate that the necessary and sufficient condition to stabilize the system is L <;; 3/2 + √2, where L is the Lipschitz constant describing the size of the uncertainty of the nonparametric part. This critical value is the same as that first obtained in [8] for a class of purely nonparametric systems, which shows that the capability of feedback is not influenced by the parameterized uncertainty in the systems, as long as the corresponding parametric function is bounded by the linear growth rate.