Design Of Reduced Order Unknown Input Observer For Markov Jump System

In the past few decades,there have always been random mutations in the input and internal variables in some actual systems,such as component maintenance,random failures,sudden environmental changes,etc.These dynamic systems can be jumped by Markov System representation.As a special kind of hybrid system,the Markov jump system has its parameters changing with the development of a finite Markov chain.Compared with the limitations of the single-mode system,it is more attractive to people.And used in manufacturing systems,communication systems,aerospace systems,etc.Importantly,most of the existing theoretical results of Markov jump systems are based on known transition probability.In practical applications,it is extremely difficult to obtain transition probability.Therefore,consider the Markov jumps whose transition probability is partially unknown.The variable system is extremely important.On the other hand,most studies on stability analysis of Markov jump systems are based on infinite time domain research,but in many practical applications,for example,in electric power production and consumption systems,communication systems,and chemical systems,people only focus on transient response systems.The state within a finite time,Therefore,the transient response of the system state within a finite time range has become a hot topic for researchers.In this paper,we study the design problems of dimensionality reduction unknown input observers for discrete-time and continuous-time Markov jump systems,and give the sufficient conditions for the existence of the observer.The Lyapunov stability theorem proves the finite-time stability of the system.Finally,simulation is used to verify that the proposed method is feasible.The specific work is as follows:(1)A reduced order observer of Markov jump system with unknown input is designed.First,a new reduced order observer is designed for the system,and the unknown input is eliminated by constructing the observer gain matrix.Then,the existence of the observer is proved by derivation,and it is proved that the observer error can be stable within a limited time range,so that the system is transiently stable.Finally,an example is used to verify the effectiveness of the proposed method.(2)Discuss the state interval estimation problem of the reduced order observer of the discrete-time Markov jump system.First,design a reduced order unknown input observer to complete the state observation of the system.By selecting the appropriate Lyapunov function,the stability criterion of the error system is obtained,and the sufficient conditions for the existence of the observer are given through theoretical derivation.Then,on the basis of the reduced order observer designed in this paper,the centrally symmetric multicellular method is used to approximate the state boundary and achieve the interval estimation of the system state.Finally,by comparing with the estimation methods in other documents,it reflects the validity and generality of the theoretical results in this chapter.(3)For the Markov jump system with unknown input and time-varying generally uncertain transition rate,firstly,a design method of reduced order unknown input observer is given,which can avoid the equality constraints in the process of decoupling unknown inputs.Then the offline quantization mechanism is used to process the time-varying generally uncertain transition rate,and the number of linear matrices obtained is guaranteed to be limited,so as to solve the stability analysis problem of the time-varying Markov jump system,which has lower conservativeness.Secondly,by selecting an appropriate Lyapunov function,the conditions that the system needs to be satisfied for finite time stability are given.Finally,the rationality of the proposed method is verified by numerical simulation and example simulation.