Optimal Control of Linear Nonstandard Singularly Perturbed Discrete Systems

This paper introduces the definition of the nonstandard linear discrete-time singularly perturbed system and then shows how to solve the corresponding linear-quadratic optimal control problem since the methodology that exists in the literature for the solution of the standard singularly perturbed discrete linear-quadratic optimal control problem can not be extended to the corresponding nonstandard counterpart. The solution of the optimal control problem is obtained in terms of the pure-slow and pure-fast, reduced-order, continuous-time, algebraic Riccati equations. An example is included to illustrate the efficiency of the proposed method.