LQG control for nonstandard singularly perturbed discrete time systems

Abstract

In this paper we present a control method and a high accuracy solution technique in solving the linear quadratic Gaussian problems for the nonstandard singularly perturbed discrete time systems since the methodology that exists in the literature for the solution of the standard singularly perturbed discrete time linear quadratic Gaussian optimal control problem can not be extended to the corresponding nonstandard counterpart. The solution of the linear quadratic Gaussian optimal control problem is obtained by solving the pure-slow and pure-fast, reduced-order, continuous-time algebraic Riccati equations and by implementing the pure-slow and pure-fast, reduced-order Kalman filters. An example is provided to illustrate the efficiency of the proposed method.