Controller Design Of Several Markovian Jump Systems

With the development and application of control theory in various fields,experts have found that many practical systems are commonly experiencing sudden changes in parameters or structures,due to aging components and system internal faults,etc.These systems are usually modeled as hybrid systems.They have been applied more and more widely with the development of technology.It is well known that the Markovian jump system is a special hybrid system and involving two-part mechanisms.One mechanism is time-evolving and related to system state over time.The other one is an event-driven mechanism and named as operation mode driven by a Markov chain.Because the Markovian jump system is suitable for describing the dynamic system in engineering applications,it has certain research value and significance in the field of control.Meanwhile,the stability problem is very important and has been widely studied.It is also well known that controller design is one of the important strategies to ensure system stability and has a better calming effect in practical applications,whose form is also varied.Therefore,when considering the different control problems encountered by the Markovian jump system,designing a controller to ensure the stability of the system is worth studying.In this paper,through the Lyapunov function and transfer matrix to study the controller design problems of several Markovian jump systems and the main results as follows:(1)The problem of guaranteed cost control for a class of Markovian jump systems in the case of controller failure is studied.Different from the traditionally guaranteed controller,a kind of failure-tolerant controller is proposed.Particularly,the dwell times of controller suffering failures or not are constants.A Lyapunov function approach is used to analyze its stability,which could lead to convex conditions depending on such dwell times.Since these conditions are LMIs,the control gain can be easily calculated by using them.Finally,the LMI of the convex condition is carried out and two simulation cases are used to verify the accuracy of the conclusion.(2)Consider a class of Markovian jump system with stochastic switching,and study the exponential almost sure stability and stabilization.Sufficient conditions for EAS stability are established by using a method on its stochastic transfer matrix.Particularly,both sojourn times and distribution properties of such stochastic switching are considered,that are used to design a state feedback controller which could bear unmatched or asynchronous modes.It can be seen that our results are more general but less conservative.Some of them include previous work as special cases.Finally,it can be found that the designed controller will have a more ideal control effect no matter in simulation or theory by comparing it with several kinds of literature.(3)For the stability analysis and controller design problems of singularly perturbed jump systems(SPJSs)are studied.Here,the singularly perturbed parameter(SPP)is also with Markov switching and satisfies any (?) with positive bound (?) pre-defined.Firstly,stability conditions expressed (?)-free but involving its bound are developed by constructing an _i-dependent Lyapunov function.Secondly,a state feedback controller based on singularly perturbed jump parameters is designed to stabilization the closed-loop system.Moreover,some special cases about deterministic SPP are considered too.Finally,numerical simulation is carried out by using the conclusions in this paper,and the feasibility and superiority of the proposed method are proved by comparing with the existing methods in other literatures.