Robust Control Of Singular Markovian Jump Systems

Singular systems are found in engineering systems (such as electrical circuit andpower systems), biological systems, network, chemistry, social systems and economicsystems, etc. In many articles, singular systems are also called descriptor systems, im-plicit systems, generalized state-space, differential-algebraic systems or semi-state sys-tems. Singular systems is a better one for describing physical systems. If the derivativematrix is invertible, they are state-space systems. Otherwise, they are a singular one.Markovian jump systems are hybrid systems with Markov jump parameters. Ev-ery subsystems of the system are deterministic, but switching of these subsystems aretriggered by Markov processes, or its state space involves Euclidean space Rn and fi-nite discrete events space S. Furthermore, the singular Markovian jump system hasbeen also considered recently. This system has a complicated hybrid information struc-ture. Consider such system, the research problem and solution is not mean the simplecombination of singular systems control theories. The singular jump system may beunstable while every subsystems are stable. The investigation of singular Markovianjump systems is a new and challenging problem.In this article, problems of robust control for linear continuous singular Markovianjumpsystemsareconsidered. Themainproblemandcontributionofthedissertationareas follows:·The basic conception of singular Markovian jump systems is given. Series ofdefinitionsarepresented. Thebackgroundandsignificanceofthesystemareintroducedcompletely. The situation of this system is analyzed. , and the research object andresearch solution are given too.·For uncertain singular jumping systems with time-delay, the derivative matrixis certain, but the parametric and the transition rate's uncertainties are assumed to benormbounded. ByconstructingastochasticLyapunov-Krasovskiifunctional,sufficientconditions are provided such that the system is regular, impulse-free and stochasticallystable in mean square sense for all admissible uncertainties.·For uncertain singular Markovian jump systems, the uncertainties are unknowntime-varying but norm bounded. The system is transformed into a equivalent one bypremultiplying and postmultiplying matrices. By constructing a stochastic Lyapunov-Krasovskii functional, Sufficient conditions are given and the controllers are designedsuch that the system is regular, impulse-free and stochastically stable in mean square sense for the uncertainty.Based on our obtained results, numerical examples are given to demonstrate theeffectiveness of the proposed methods.Finally, thisdissertationhasbeenconcluded, andseveralfurtherresearchproblemsare also given.