Study On The Observation Method Of Discrete-time Nonlinear Markov Jump Systems

In recent years,Markov jump systems has gradually become a hot research object in the fields of mathematics and control.At the same time,the state observation of the system is an important annulation to realize the subsequent control of the system.Numerous of research results have been achieved based on the state observer design method.However,the Markov jump systems considered in the existing observer design is mostly a relatively idealized model.In practical application,it is inevitable that more general conditions will appear,which will become the interference elements of the state estimation.To solve this problem,this thesis considers a more general system model,The nonlinear Markov jump system is described by Takagi-Sugeno fuzzy model.Then linear system theory is applied to estimate the internal state of the system.The main work includes:The state equation of Markov jump system with unknown input in general sense is analyzed.In this case,the unknown input observer of the system is designed.The sufficient conditions and proof for the existence of the observer are given.Finally,the validity of the theorem is verified by an example simulation.For a generalized Markov jump system with unknown inputs in both the state equation and the output equation,an observer with a relatively new form structure is proposed.The sufficient conditions for the existence of observer are given by using Lyapunov function and the related theorems are derived.A numerical example is given to prove that the observer designed by this proposed method can track the actual state of the system accurately.The estimation error converges to zero.Finally,extending the study to a more general situation,For generalized Markov jump systems,the actuator fault is also considered in the equation of state while the unknown input is considered.Sufficient conditions for the existence of the unknown input observer are derived by selecting appropriate fuzzy quadratic Lyapunov function.The observer can still estimate the state of the system when the fault occurs and reconstruct the system faults.On this basis,an example of a nonlinear tunneling diode circuit is introduced to verify the feasibility of the proposed method.From the simulation results,the internal state of the system and the actuator failures can be well estimated,so the observer design is successful.