Researches Of Robust Control For Structure Uncertain Linear Systems

The major topic of control problems is to modify the dynamics of a system such that some particular objects are satisfied. Control theory is benefited from practical activities and will be used to solve practical problems. Based on precise mathematical models, classic linear control theory tries to find a controller satisfying given performance index, while modern control theory aims to search the optimal controller such that the optimal performance index can be realized. However, almost all of real systems may suffer uncertainties in different forms. The uncertainties include either model imperfections, such as unmodeled dynamics, parametric uncertainties, change of the operating environment, model reduction and linearization approximations, etc., or external disturbance, for example, various disturbance with unknown statistical characteristic and bounded energy. For the analysis and synthesis of uncertain systems, this dissertation admits some tolerance of uncertainties, within which robust performances are guaranteed. Moreover, by optimization, the upper or lower bounds of performance index can be obtained instead of index itself.The work of this dissertation mainly addresses the issues for robust control of linear uncertain systems, which include stability, quadratic stability, structured stability, H control, region pole location, etc..In detail, the major contributions of this dissertation as follows:1. Establishing a sufficient condition for the Schur stability based on the radius of robust stability of Schur-Cohn polynomial. Then, using the above result to establish a necessary and sufficient condition for the robust Schur stability of interval polynomial and an algorithm to check the Schur stability of interval polynomial.2. Transforming the problem of robust Hurwitz and Schur stability of interval system into checking the nonsingularity of a set of uncertain matrices, then establish necessary and sufficient conditions for the robustHurwitz and the robust Schur stability of interval system base on -analysis.3. A new sufficient LMI condition for the robust stability is established with respect to polytopic uncertainty. The robust stability can be verified by means of the feasibility of a set of LMIs described only in terms of the vertices of the polytopic domain. The approach is less conservative than quadratic stability by using a parameter-dependent Lyapunov function and extends the results of the related references.4. An explicit expression to compute H norm and obtain H controller, which are recently obtained for continuous-time state-space symmetric systems, are extended to more general case of continuous-time symmetric systems. The computations of H norm only need to compute the maximum eigenvalue of a symmetric matrix, which only contains the system matrices.5. An explicit expression to compute the H norm of the discrete-time symmetric system is established using the Bounded Real Lemma. One explicit solution of stabilizing output feedback gains is obtained for the output feedback stabilization problem. Ah explicit expression for H norm and the sub-optimal output feedback controllers have been obtained for the H control problem.6. Considering the structural stability problem for continuous-time descriptor systems with real convex polytopic uncertainties, an LMI sufficient condition, which is simply and efficiently computable, is established for checking the robust admissibility is proposed, and a special case E = diag(I,0) is investigated.7. An LMI's DL -admissible condition for descriptor systems and robustly DL -admissible condition for polytopic uncertainty are established. Then, we establish an DR -admissible condition and a robustly DR-admissible condition for descriptor systems with polytopic uncertainty. The results of this paper extend the existed results of normal systems to descriptorsystems.8. Lower and upper matrix bounds for the positive semidefinite solution of discrete-time Riccati matrix equation are ob...