State Feedback Controller Design For Piecewise Homogeneous Markov Jump Systems Subject To Actuator Saturation

Markov jump system is a new field of research in complex system modeling and control.Various pratical systems,such as manufacturing system,communication network,robotic system as well as economic system,which frequently experience abrupt variations in their structure and parameters due to random factors,can be described by Markov jump model.Most of the previous analysis and synthesis about Markov jump systems presume that the transition rates are time-invariant,that is,the Markov process is homogeneous.However it is hard to keep the transition rates invariant during the running process practically.Some typical examples can be found in component failure rate of systems engineering,the packet dropouts and channel delays in Networked Control Systems,economic growth model,and so on.The transition rates are time-variant owing to random factors.To better model the practical situation mathematically,the piecewise homogeneous Markov jump system was proposed.Such system is characterized by its piecewise time-varying transition rates.However,research in this field remains at a relatively early stage.Actuator saturation is probably the most common nonlinearity in the pratical engineering systems and can severely degrade the performance of closed-loop systems.If the controller is designed without considering the actuator saturation,it may even make a stable closed-loop system unstable.Moreover,time-delay is inevitable in the real world,which is the cause of instability and performance degradation.In recent years,saturation control of Markov jump system has been a research problem in the area of control theory and practice.Although some relevant papers take into account the cases in which transition probabilities are partly unknown or completely unknown,few researches consider its time-varying characteristic.Therefore,this paper mainly focuses on the stability analysis and saturation control of piecewise homogeneous Markov jump system.Main contents of this paper are as follows:1.The design of state feedback controller and estimate of the domain of attraction for piecewise homogeneous Markov jump system subject to actuator saturation are investigated.Firstly,The stabilization problem is solved by designing state feedback controller which guarantees the stochastic stability of the closed-loop system.Then,we use the intersection of ellipsoid invariant set under different modes to estimate the domain of attraction and obtain the maximum domain of attraction and the state feedback controller gain by solving the convex optimization problem with linear matrix inequality constraints.2.Stochastic stability,design of state feedback controller and estimation of the domain of attraction for piecewise homogeneous Markov jump system with actuator saturation and time-varying delay are investigated.Firstly,for piecewise homogeneous Markov jump system with time-varying delay,less conservative delay-dependent stochastic stability conditions are presented by introducing matrix variables related to system modes and stochastic variation of transition probabilities into Lyapunov-Krasovskii functional.Secondly,considering the problem of stabilization with iuput saturation,a set of mode-dependent ellipsoid invariant sets is introduced to construct the stochastic stability region and delay-dependent stochastic stabilization conditions are obtained by designing state feedback controller.Finally,the state feedback controller gain and the maximum domain of attraction are solved using convex optimization.