Design of Output Feedback Controllers for Robust Stability and Optimal Performance of Discrete-Time Systems

This paper presents an algorithm for the design of robust output feedback controllers for linear uncertain discrete-time systems. The algorithm utilizes a version of the BFGS method of conjugate directions and minimizes a performance index that includes an LQR term to optimize performance and a robustness term which is based on recently developed bounds. The minimization of only the robustness term which corresponds to the maximization of the uncertainty bound is also studied. The case of unstructured perturbations in A has been the only one studied in the literature; the present algorithm not only introduces a uniied approach to both unstructured and structured perturbations in A but also is shown to improve considerably the unstructured uncertainty bound for the system matrix A found in the literature. Additionally, several other cases involving unstructured/structured perturbations in all the state-space matrices are exploited and numerous examples are provided to illustrate the results.