Analysis And Synthesis Of Markovian Jump Hybrid System

Markovian jump linear systems (MJLs) have a strong practical background, sincein practice many physical systems are subjected to abrupt variations in their structuresand parameters, due to random failures or repairs of components, changing subsysteminterconnections, sudden environmental disturbances, etc. Due to extensive applicationsof such systems in many practical engineering, MJLs have been drawing continual in-terest from control theorists and engineers. On the other hand, the violent developmentof high-tech makes large number of controlled plants in industrial processes, productionequipment, etc, become more large-scaled and complicated, and the dimension of thesystem tends to be higher and higher. Therefore, in order to establish more precise mathe-matics model for controlled plant or system process, we should not only apply Markovianjump system model, but also other mathematics models, such as stochastic system model,singular system model, LPV system model, networked control system model and so on.Therefore, Markovian jump hybrid system (stochastic Markovian jump system, singularMarkovian jump system, LPV Markovian jump system, network-based Markovian jumpsystem, etc.) arises, which has attracted lots of attention of many scholars. Thus, it is ofgreat theoretical and practical significance that research on the Markovian jump hybridsystems.The emphasis in this thesis is focused on the studies of H_∞control, H_∞filteringand fault detection problem for Markovian jump hybrid systems. There are some complexdynamic systems considered here, such as, time-delay Markovian jump system, stochasticMarkovian jump system, network-based singular Markovian jump system and network-based LPV Markovian jump system. The main contents are as follows:1. First, we overview the background and significance of Markovian jump hybridsystems, then summarize the recent study status of many important Markovian jump sys-tem, from which we can find some problems to be further studied. Then summarize theadvance, standard problems and the basic techniques of linear matrix inequality (LMI).Finally, introduce the main contents and the background of several important problems inthis thesis.2. Robust H_∞control and filtering problem for uncertain discrete-time Marko- vian jump systems with mode-dependent time delay is investigated. Based on a new typeof Lyapunov functional, delay-dependent condition for robust stability of the system isderived, robust stabilization controller and robust H_∞controller and H_∞filter are subse-quently designed.3. Robust passivity analysis and robust passive control for uncertain Markovian jumplinear systems with time-varying delay is concerned. By constructing a proper stochasticLyapunov-Krasovskii functional and employing slack matrix technique, delay-dependentpassivity performance conditions are formulated in terms of linear matrix inequalities.Based on this condition, the passive controller is designed.4. Robust H_∞filtering for a class of uncertain stochastic Markovian jump systems isstudied. The system under consideration contains Ito?-type stochastic disturbances, time-varying delays and involves norm-bounded uncertainties both in the system matricesand in the mode transition rate matrix. By constructing a proper stochastic Lyapunov-Krasovskii functional, Ito? formula and employing slack matrix technique, sufficient con-ditions that guarantee the filtering error system stochastically stable and satisfy a pre-scribed H_∞disturbance rejection attenuation level. Then based on the condition, thedesired roust H_∞filter is designed in terms of LMI.5. The problem of fault detection for discrete-time Markovian jump singular sys-tems with packet dropout is investigated. A stochastic variable satisfying the Bernoullirandom binary distribution is utilized to model the phenomenon of data missing. Since theresidual system becomes a Markovian jump singular system with stochastic parameter inthe system matrices, definition for stochastic parameter varying Markovian jump singu-lar system (SPVMJSs) is introduced. And new definitions of stochastic Markovian jumpstable and stochastic Markovian jump admissible for such systems are introduced. Bythe definitions, Lyapunov functional and slack matrix technique, necessary and sufficientcondition for the resulting system to be stochastic Markovian jump admissible is proposedin terms of strict LMIs. Then, based on this condition, the H_∞performance condition ofSPVMJS system and the desired fault detection filter is subsequently designed.6. Quantized H_∞filtering for a class of discrete-time LPV systems with Markovianswitching under packet dropout is investigated. Based on multiple Lyapunov functionalmethod, sufficient condition that is derived for the existence of the filter, such that the fil-tering error dynamics is stochastically stable and the prescribed noise attenuation levels in H_∞sense can be achieved, in terms of parameterized linear matrix inequalities (PLMIs).Then, based on the condition, H_∞filter is designed. Finally, by means of approximatedbasis functions and gridding technique, the obtained PLMIs are transformed into LMI,which can be solved efficiently.