Stability Analysis And Research On Related Control Problems For Singular Systems

Singular system theory was proposed in seventies of the 20th century, since its good application background, much attention has been paid to its theory research and applica-tion; it has been an important branches of modern control theory. Time delay is inevitable in real engineering systems, and it may lead to instability or performance deterioration of control systems. Singular time-delay systems are more general than normal delay systems, and under some conditions, normal delay systems can be regarded as a special case of singular time-delay systems; what is more, some problems can only be described by singular delay systems. Recently, there have been great development on fundamen-tal theory and stability of singular time-delay systems, however, there still exist certain limitations, and such theory needs to be developed further.Based on singular time-delay systems, this dissertation studies the problems of sta-bility,H∞control, guaranteed cost control and H∞control for T-S fuzzy singular systems.The main contents of this dissertation include:(1) The research background of this dissertation is introduced. Firstly, the research background of singular systems theory, structure characteristics and significance are sum-marized, the development states of singular time-delay systems are introduced in detail, and some real examples are given to show the usefulness of singular time-delay systems; then, the research states, methods and obtained results about singular time-delay systems stability,H∞control, T-S fuzzy singular systems are presented, and the problems need to be improved are also highlighted; lastly, the main work of this dissertation is introduced.(2) The stability of continuous and discrete singular time-delay systems is stud-ied. For continuous singular delay systems, the equivalence of some existing stability conditions are proved, and the specific description is also presented; by using delay de-composition method, a less conservative stability condition is obtained; and then, new stability conditions for discrete singular time-delay systems are proposed.(3) H∞control for singular time-delay systems with constant delay is studied. By eliminating redundant variables, new concise delay-dependent bounded real lemma(BRL) conditions are derived; on the basis of introducing a regulation parameter, an improved H∞control method is obtained. Compared with the existing results, the newly obtained control conditions include no any free-weighting matrices, and the obtained conditions will introduce less conservatism and less computational complexity; the design method of robust non-fragile controller is proposed, which can be converted into the solvability of linear matrix inequalities, and some existing results in the literature are also extended.(4) H∞control for singular systems with time-varying delay is studied. By com-bining linear matrix inequalities, Jensen integral inequalities and delay decomposition, this dissertation analyzes the performance of systems, and linear asymptotic stable filter-ing is designed, the existence conditions for filter are also given.(5) The problem of robust control for uncertain linear singular systems with state delay is discussed. The design method of robust passive controller is proposed; observer-based optimal guaranteed cost controller design for singular systems with parameter un-certainties and state delay is proposed, for all admissible parameter uncertainties, the de-signed controller can guarantee the robust stabilization and optimal quadratic-guaranteed-cost of singular delay systems.(6) By defining corresponding fuzzy Lyapunov function and introducing slack variables, this dissertation studies continuous and discrete T-S fuzzy singular systems. The newly obtained stability conditions are less conservative than the fundamental ones. To avoid BLMI in the literature, the newly obtained stability conditions can be converted into simple LMI, which can be solved by Matlab LMI control toolbox effectively.(7) Finally, the results of the dissertation are summarized and further research topics are pointed out.