Control And Filtering For Continuous-time And Discrete-time Positive Fuzzy Markov Jump Systems

Positive fuzzy Markov jump systems are a class of dynamic systems with three characteristics of positivity,nonlinearity and stochastic jump.Due to the extensive applications in modeling practical systems in industry,medicine and ecology,positive fuzzy Markov jump systems have received increasing attention.This thesis is concerned with the problems of control and filtering for discrete-time and continuous-time positive fuzzy Markov jump systems by using the linear programming method.Some stability and performance criteria are derived,and then the existence conditions and design methods of the l1(L1)-gain positivity preserving fuzzy controllers and filters are presented in the form of linear programming.Some numerical examples are given to verify the effectiveness of the results.This thesis contains the following three chapters.Chapter 1 introduces the research background of this thesis.The devel-opment history and research status of positive fuzzy Markov jump systems are described,and the research gap of such systems is pointed out.Then the structural framework and main work of this thesis are briefly introduced.In Chapter 2,the design problems of the l1-gain positivity preserving fuzzy controller and filter are studied for a discrete-time positive fuzzy Markov jump system.First,the definitions of stochastic stability and l1-gain performance are given.Then based on the above definitions,by constructing a co-positive Lyapunov function,the stochastic stability and the l1-gain performance of the discrete-time positive fuzzy Markov jump system are analyzed.Some criteria are given in the form of linear programming which guarantee the system is positive,stochastically stable and satisfies the prescribed l1-gain performance index.Moreover,a class of l1-gain positivity preserving fuzzy controllers and filters are constructed with the existence conditions provided.Then the con-troller and filer design problems can be converted into solving standard linear programming problems.In Chapter 3,for a continuous-time positive fuzzy Markov jump system,the definitions of exponential mean stability and Li-gain performance are giv-en,and then some sufficient conditions for the positivity,exponential mean sta-bility and Li-gain performance are obtained in terms of linear programming.Furthermore,the design problems of a class of L1-gain positivity preserving fuzzy controllers and filters are solved.