At first, this paper introduced the current research status of singular sys-tems and singular Markov jump systems, as well as the nonlinear Markov jump systems. This paper mainly discussed the robust H∞ filtering problem for a class of nonlinear uncertain discrete-time singular Markov jump systems.Chapter 2 discussed the robust H∞ filtering problem for a class of nonlin-ear uncertain discrete-time singular Markov jump systems, where the nonlin-ear function satisfies a quadratic constraint and the uncertainties are parameter bounded. By using the linear matrix inequality(LMI) technique, a sufficient condition is proposed to guarantee the nominal singular Markov jump filtering error system is regular, causal, has unique solution in a neighborhood of the equilibrium point, is stochastically stable and satisfies H∞ performance. By using this condition and a series of matrix inequalities, another LMI sufficient condition is derived to guarantee the nominal singular Markov jump filtering error system is regular, causal, has unique solution in a neighborhood of the equilibrium point, is stochastically stable and satisfies H∞ performance. Then, the design method of robust H∞ filter is given, the filter obtained can be full order or reduced order standard Markov jump system. A numerical exam-ple is provided which verifies the correctness and effectiveness of the method proposed in this paper.Chapter 3 discussed the robust H∞ filtering problem for a class of nonlin-ear uncertain discrete-time singular Markov jump systems with time-varying delay, where the nonlinear function satisfes a quadratic constraint. A sufficient condition in the form of LMI is presented to guarantee the nominal singular Markov jump filtering error system is regular, causal, has unique solution in a neighborhood of the equilibrium point, is stochastically stable and satisfies H∞ performance. In order to facilitate the design of the filter, by using this con-dition and a series of matrix inequalities, another LMI sufficient condition is derived to guarantee the nominal singular Markov jump filtering error system is regular, causal, has unique solution in a neighborhood of the equilibrium point, is stochastically stable and satisfies H∞ performance. Then, the design method of robust H∞ filter is given, and this filter can be full order or reduced order standard Markov jump system. A numerical example demonstrated the correctness and effectiveness of the proposed method.In chapter 4, a brief summary is given for the studied problems, the rele-vant theories,as well as the used methods and the research ideas. |