High-performance simultaneous stabilizing periodic feedback control with a constrained structure

In this paper, controlling a set of continuous-time LTI systems is considered. It is assumed that a predefined guaranteed continuous-time quadratic cost function, which is, in fact, the summation of the performance indices for all systems, is given. The main objective here is to design a periodic output feedback controller with a prespecified structure, e.g., polynomial, piecewise constant, decentralized, etc., which minimizes the above mentioned guaranteed cost function. This problem is first formulated as a set of matrix inequalities, and then by using a well-known technique, it is reformulated as a LMI problem. The set of linear matrix inequalities obtained represent the necessary and sufficient conditions for existence of the desired structurally constrained controller. Moreover, an algorithm is presented to solve the resultant LMI problem. Finally, the efficiency of the proposed method is demonstrated in two numerical examples, which are investigated in several relevant papers