The Admissibility And Dissipativity Analysis For Discrete Singular Time-delay Systems

Since the beginning of 1970 s, people started to investigate the singular system. Now singular system has a wide application in many practical systems, such as economic system, non-causal system, electrical system,complex circuit and artificial neural network, chemical system, constrained mechanical system, etc. Singular system, substantially, is the combination of differential equation set and algebraic equation set, so for singular system,apart from the stability, the regularity, absence of impulses(for continuous singular system) or causality(for discrete singular system) should also be considered. In addition, time delay exists widely in natural systems and practical engineering systems, which usually causes the system unstable and poorly performed in dynamic systems. Therefore, the study of time-delay system is very important for practice.In this thesis, some newest research approaches are utilized to study the issue of admissibility analysis, robust H_∞control and dissipativity analysis for singular system. Given by strictly linear matrix inequality(LMI), all of the results are less conservative than the present newest research results in such field. The main research contents are presented as follows.(1) The problem of admissibility analysis for discrete singular system with time-varying delays is studied. The main contribution of this paper is to reduce the conservatism of the considered system by adopting an improved reciprocally convex combination approach to bound the forward difference of the double summation term, and utilizing the reciprocally convex combinationapproach to bound the forward difference of the triple summation term in the Lyapunov function, together with free-weighting matrix, Jensen inequality,etc.(2) The problem of robust H_∞ control for discrete singular system with norm-bounded uncertainties and time-varying delay is studied. Based on a novel bounded real lemma, a sufficient criterion for the existence of the H_∞ state feedback controller is given in the form of matrix inequalities with nonlinear constraints, through adopting improved reciprocally convex combination approach and LMI technique. Then, the cone complementarity linearization(CCL) method is adopted to solve the nonlinear constraints and get the H_∞ state feedback controller.(3) The problem of dissipativity analysis for discrete singular system with time-varying delay is studied. By using a recently developed integral inequality and the improved reciprocally convex combination approach,sufficient criteria are established to guarantee the admissibility and dissipativity of the considered system. Moreover, H_∞performance characterization and passivity analysis are carried out.