Non-fragile Control Of Positive Markovian Jump Systems

In the real world,many dynamic systems can be modeled as a kind of hybrid systems whose state variables and outputs are always nonnagetive.This kind of systems is called positive systems.They have widely applications in biomedicine,communication,ecology,and other fields.Positive Markovian jump systems are a special class of Markovian jump systems,whose subsystems are all positive systems.They have been verified to be available to describe various systems,such as economic systems,power systems,networked control systems,etc.In practice,actuator faults and the fragility of controllers are unavoidable due to actuator degradations,the limited capacity of various components and complex environmental factors.Therefore,the non-fragile control of positive Markovian jump systems with actuator faults is of great theoretical and practical significance.This thesis mainly studies the non-fragile saturation control of positive Markovian jump systems(positive semi-Markovian jump systems)with actuator faults and actuator saturation.The specific content is as follows:Chapter 1 first introduces the research background and significance of the subject.Then the research status of positive systems and positive Markovian jump systems are summarized.Furthermore,the recent development of the actuator faults,saturation,and the non-fragile control is introduced.Finally,the main research contents of this thesis are summarized.Chapter 2 studies the non-fragile control of positive Markovian jump systems with actuator faults.First,a non-fragile controller structure composed of nominal controller and gain perturbation term is proposed.Then,by using the stochastic co-positive Lyapunov function,a sufficient condition is established to guarantee the stochastic stabilization of the systems.The controller gain and gain perturbation matrix are designed based on matrix decomposition technique and linear programming approach.Furthermore,the proposed controller design approach is extended for discrete-time systems.Finally,it is verified that the designed controller is more efficient than existing ones.Chapter 3 investigates the reliable saturation control of a class of nonlinear positive Markovian jump systems with randomly occurring actuator faults.It is assumed that the actuator faults depend on a Markovian process.First,sufficient conditions for stochastic stability of nonlinear positive Markovian jump systems are established using stochastic co-positive Lyapunov function.Then,the L1 control synthesis of nonlinear positive Markovian jump systems with actuator faults and saturation is proposed.Furthermore,the controller gain and the attraction domain gain are designed respectively by means of matrix decomposition technique.Finally,the maximum attraction domain is estimated by linear programming.Chapter 4 first discusses the non-fragile control of positive semi-Markovian jump systems with actuator saturation.A kind of non-exponential distribution is chosen as probability distribution of sojourn-time.The non-fragile controllers of the systems with/without interval uncertainties are designed by means of matrix decomposition technique,respectively.An optimization method based on linear programming is proposed to estimate the maximum attraction domain.Then,a time-varying and bounded transition rate is introduced,which satisfies the mode transition-dependent sojourn-time distribution.By constructing a stochastic co-positive Lyapunov function and using matrix decomposition technique,the reliable controller of positive semi-Markovian jump systems is designed.Furthermore,such controller design approach is extended for positive semi-Markovian jump systems with interval and polytope uncertainties.Finally,a reliable control design approach with less conservativeness is proposed using the segmentation technique of transition rates.Chapter 5 sums up the research contents and puts forward some further issues.