Output feedback controller design for discrete LTI systems with polytopic uncertainty via direct searching of the design space

Abstract

AbstractThis paper concerns static output feedback stabilization of polytopic discrete linear time‐invariant (LTI) systems. The previous related studies were mainly based on linear matrix inequality (LMI) approaches which are naturally conservative. In this paper, a novel design algorithm is presented that iteratively partitions a primary design space to subspaces. Then, by assessing stabilizability status of each generated subspace, the algorithm determines the total stabilizable parts and removes the undesired parts of the design space. Mathematical theories are developed to determine the total de‐stabilizability or stabilizability of a given subspace. These subspaces' properties are detected through checking the existence of critical polynomials (which have roots on the unit circle of the complex plane) on their exposed edges. By omitting the undesired parts of the design space, the algorithm just searches the desired parts which are far smaller than the primary design space. This strategy improves the feasibility performance of the algorithm. Some illustrating examples are provided to show the steps of the design algorithm. Furthermore, 100 random models are generated to evaluate the feasibility performance of the proposed algorithm as compared to some existing methods. The results reveal the superiority of the proposed algorithm.