Static Output Feedback Robust Optimal Control Based On Structured Lyapunov Matrix

Static output feedback control is one of the most basic issues in control theory and application. For actual systems, the state variables are usually difficult or costly to measure. Output feedback control is often adopted to deal with this condition. Static output feedback control has simple control structure and simple physical implementation, as well as low cost and high reliability. In addition, lower-ordered dynamical output feedback control problem also can be translated into specific form of static output feedback control problem. Therefore, the problem of static output feedback control has quite important theoretical significance and practical value.In this thesis, the problem of static output feedback stabilization is mainly considered for linear systems. After appropriate coordinate transformation, the problem of static output feedback stabilization is translated into convex optimization problem of solving linear matrix inequalities (LMIs) based on assigning a particular structure to a Lyapunov matrix. Furthermore, the sufficient conditions for the existence and design methods of the controllers are proposed. Main achievements are as follows:First of all, the problem of static output feedback stabilization for linear time-invariant (LTI) systems is studied. An algorithm is given based on proposing a structured Lyapunov matrix, which is also applied on designing H∞controller, H2 controller and mixed H2/H∞controller. The output feedback gain can be solved directly by LMI approach.Secondly, for norm-bounded parameter uncertainty linear systems, a sufficient condition of the solvability for the stabilization problem is put forward based on structured Lyapunov matrix and S-procedure. Furthermore, the design methods of robust H∞controller, H2 controller and H2/H∞optimal guaranteed cost controller are proposed in terms of LMIs.Finally, the problem of static output feedback stabilization and design methods of H∞controller and H2 controller are studied for discrete-time linear systems. A stabilization algorithm is given in terms of LMIs by imposing a particular structure on the apunov matrix, and then the algorithm is extended to the design of H∞controller and H2 controller.The core of this thesis:after proper coordinate transformation, the problem of static output feedback is translated into optimization problem of LMIs that is easy to solve by proposing structured Lyapunov matrices.The feasibility and effectiveness of all the conclusions above are demonstrated by simulation examples.