Computational Algorithms for Optimization Problems for Periodic Systems

Abstract. We give a survey of computational algorithms derived in a series of papers for solution of a synthesis problem for optimal stabilization of periodic systems. The proposed algorithms synthesize reliable control, with a given stability tolerance, for periodic systems optimized with respect to the quadratic performance criterion. A reliable controller guarantees the stability and is nearly a linear/quadratic regulator. We also consider the inverse problems for optimal synthesis corresponding to quadratic functionals. The algorithms designed to solve this problem are based on methods of linear matrix inequalities. The efficiency of the proposed algorithms are shown through implementing some examples. In this note we give an overview of computational algorithms for solution of a synthesis problem for optimal stabilization of periodic systems. Our study is based on stability of a discrete algebraic Riccati equation (ARE). The main feature of this study is to define an optimal regulator for linear discrete periodic control systems and minimize the corresponding quadrati