Robust Control For Linear Singular Time-Delay Systems

In this dissertation, the problem of robust control for linear singular time-delay systems is researched. The delay-dependent robust stability criteria for two classes of uncertain singular time-delay systems are presented. The problem of state feedback robust stabilization and dynamic output feedback robust stabilization and the problem of delay-dependent robust resilient H_∞ control are considered. A delay-dependent bounded real lemma (BRL) is obtained. Finally, the observer design and fault detection and isolation (FDI) are researched. There are five chapters in this dissertation.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, H_∞ control, observer design and fault detection, which are all the hot subjects for research in this field. Then the study for singular time-delay systems, including the structure characteristics, existence, uniqueness and stability of solutions, and observer design are discussed. Some open problems in this field are pointed out as well. Finally, the main work of this dissertation and the used notations are listed.In Chapter 2, the delay-dependent robust stability criteria are investigated for two classes of uncertain singular time-delay systems with norm-bounded uncertainties. By using the Lya-punov technique and introducing a new Lyapunov-Krasovskii functional, for the first time in the world, a delay-dependent stability criterion in terms of linear matrix inequalities (LMIs) is established for the nominal singular time-delay system, which guarantees the system to be regular, impulse free and asymptotically stable. Thus we can carry on effective judgement for the stability of singular time-delay systems with different delay bounds by using the delay-dependent stability criterion and the LMI Toolbox in MATLAB. Then, based on this criterion and the concept of generalized quadratic stability, the delay-dependent robust stability criteria for two classes of uncertain singular time-delay systems are proposed. The novelty of this chapter is the delay-dependent stability criterion for singular time-delay systems, which in essence improves the delay-independent stability criterion presented by [1] and [2] independently in 2002. This criterion, with delay-dependent robust stability criteriaobtained afterwards in this chapter, has established the foundation for designing the robust stabilizing controller and robust resilient H^ controller in the next two chapters. Two numerical examples are given at the end of this chapter to illustrate the effectiveness and less conservatism of the proposed method.Chapter 3 is devoted to the problem of delay-dependent robust stabilization for two classes of uncertain singular time-delay systems. All the coefficient matrices except the matrix E include norm-bounded uncertainties. Based on the delay-dependent stability criterion for the nominal singular time-delay system obtained in Chapter 1, and by using the idea of generalized quadratic stabilization, two feedback cases are discussed: state feedback case and dynamic output feedback case. The sufficient conditions for the existence of the robust stabilizing controllers are given. Aiming at the nonlinear terms and the equality constraints about the unknown variables in the sufficient conditions, we develop the classical cone complementary linearization technique proposed in [3] and convert the solving for controllers to the non-convex optimization problems. And then the cone complementarity linearization iterative algorithms are proposed to design the desired robust stabilizing controllers. Since the cone complementarity linearization iterative algorithm converges, the algorithm in this chapter for the design of the dynamic output feedback controller improves that presented in [4] to a certain extent. The novelty of this chapter is the design for the delay-dependent robust stabilizing controller. Solving the matrix inequalities containing the equality constraints and the nonlinear terms by using the cone complementarity linearization iterative algorithm, is one characteristic of the algorithm in this chapter. From the detailed numerical examples, we can see that the design algorithms are effective.In Chapter 4, the problem of delay-dependent robust resilient H^ control is discussed for uncertain singular time-delay systems. 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 #