Robust Resilient H_∞ Control For Interval Singular Systems With Time-varying Delays

In this thesis, the problem of robust resilient H_∞control for interval singular systems with time-varying delays is researched. Robust resilient control criteria for interval singular systems with time-varying discrete and distributed delays are presented. There are 3 chapters in this thesis.In Chapter 1, the background and model formulation of time-delay systems are reviewed, and some advances in the study of linear standard state space time-delay systems are recalled. They include: theory of stability. Then the study for singular time-delay systems, including the structure characteristics, existence, uniqueness and stability of solutions, H_∞control and resilient control are discussed.In Chapter 2, the problem of robust resilient H_∞control is discussed for interval singular systems with time-varying delays. The main idea is to design a resilient controller with gain variations to robustly stabilize the system, and guarantee the H_∞norm of the transfer function from the disturbance input to the controlled output of the closed-loop satisfies a prescribed H_∞level. It is well known that in practical engineering, the controller is not easy to be precise or exactly implemented, but has a certain degree of errors. Hence, it is considered beneficial that the designed (nominal) controllers should be capable of tolerating some level of the coefficient matrices and controller gain variations. To the best of our knowledge, there is no previous result on the design of delay-dependent robust resilient controller for interval singular time-delay systems.In Chapter 3, is devoted to the problem of robust stabilization for the class of interval singular systems with time-varying discrete and distributed delays. All the coefficient matrices except the matrix E are interval matrices. Based on the delay-dependent stability criterion for the nominal singular time-delay system obtained in Chapter 2, and by using the idea of generalized quadratic stabilization, the expanded case is discussed: descriptor systems with delays and controller gain variations. The considered system parameter uncertainties are norm-bounded and the time delays include both discrete delay and distributed delay. Then the sufficient conditions for the existence of the robust resilient H_∞controllers are obtained.