Construction of Lyapunov function that maximizes the parameter uncertainty that can be handled by output feedback stabilized discrete-time dynamic systems

It has been shown that if the uncertainties of a discrete-time dynamic system can be modeled by cone bounded functions of the states, that such a system can be asymptotically stabilized, depending on the size of the uncertainties, via either deterministic Lyapunov based state or output feedback. Unlike continuous-time dynamic systems, the size of the uncertainties of discrete-time dynamic systems that can be handled can not be arbitrarily large. In this paper, we present an algorithm that enables the designer to construct a Lyapunov function such that the output feedback controller derived from it is capable of handling the largest possible uncertainty, Our approach relies on the construction of a matrix Q that has a structure which facilitates the computation of the maximum uncertainty through the maximization of a judiciously chosen cost function