Linear quadratic control for singularly perturbed systems

Abstract

This paper proposes a new methodology to design a sub-optimal control for singularly perturbed systems. The controller is given in terms of the solution of a set of inequalities. An algorithm is given to solve those inequalities through LMI (Linear Matrix Inequality) formulation. An example exhibits that the results are very close to the exact optimal solutions. The main features of this approach are that it takes advantage of LMI to deal with singularly perturbed systems with less conservativeness and can be extended to other robust, and multi-objective control problems for singularly perturbed systems. In addition, it is fit, for both standard and nonstandard singularly perturbed systems.