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Robust Control for Linear Singular Time-Delay Systems

Author: ZhuShuZuo
Tutor: ChengZhaoLin
School: Shandong University
Course: Operational Research and Cybernetics
Keywords: linear singular time-delay systems delay-dependent stability criterion robust stabilization robust resilient H_∞ control unknown input observer fault detection and isolation (FDI) linear matrix inequality (LMI) cone complementarity linearization iterative algorithm
CLC: O231.1
Type: PhD thesis
Year: 2005
Downloads: 433
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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 #<? level. We focus on the resilient controllers respect to additive and multiplicative controller gain variations. 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 controller gain variations. To the best of our knowledge, there is no previous result on the design of delay-dependent robust resilient controller for uncertain singular time-delay systems. Based on the delay-dependent stability criterion for the nominal singular time-delay system obtained in Chapter 2, a new delay-dependent BRL is discussed. Then for the first time, the sufficient conditions for the existence of the delay-dependent robust resilient Hqq controllers and the design algorithms are obtained.Chapter 5 deals with the problem of observer design and FDI for singular time-delay systems, which consists of two parts. In the first part, the unknown input observer design for linear nonregular singular time-delay systems and the application of the observer in FDI are considered. The design methods of the infinite time observer and the finite time observer are presented in this filed for the first time, which can be used for the purpose of FDI. The former can converge to the state and the unknown input by exponential rate, and the latter will realize the exact reconstruction of the state and the unknown input in finite time. The coefficient matrices of the singular systems with multiple delays are described for the first time in terms of multivariate polynomial matrices in the time delay operator. Under some rank conditions about the coefficient matrices, a series of generalized coordinate changes are found to transform the singular time-delay system into a standard state space time-delay system with the column unimodularity of the observability matrix being satisfied. Then after another generalized coordinate change, a higher dimension system is got with time-delay terms associating with the input and output only in the system description. The exponential asymptotic estimation for the state and the unknown input of the singular time-delay system is realized by designing the state observer for the equivalent system. Noticing that fault inputs belong to the category of unknown inputs in essence, so the unknown input observer certainly can be used for FDI. In this chapter, based on the designed observers, for the first time, the FDI for singular time-delay systems can be realized by using two approaches respectively: the approach of estimating the fault magnitude and the approach based on residual generation. In the second part, a different design method of the robust FDI observer (RDO) for another class of singular time-delay systems is proposed. A sufficient condition for the existence of RDO and an efficient design algorithm are obtained. And the design of RDOs associated with various splitting of the faults is also given. The simulation curves of the residual illustrate the application of the proposed algorithm.Key words: linear singular time-delay systems, delay-dependent stability criterion, robust stabilization, robust resilient Hao control, unknown input observer, fault detection and isolation (FDI), linear matrix inequality (LMI), cone complementarity linearization iterative algorithm.

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CLC: > Mathematical sciences and chemical > Mathematics > Control theory, information theory ( mathematical theory ) > Cybernetics ( control theory, mathematical theory ) > Linear Control System
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