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Exponential Stability And Finite-Time Stability Of Markovian Jump Scochastic Impulsive Sytems

Posted on:2015-08-31Degree:MasterType:Thesis
Country:ChinaCandidate:C H WeiFull Text:PDF
GTID:2298330431990210Subject:Applied Mathematics
Abstract/Summary:PDF Full Text Request
Many physical systems undergo abrupt changes in their structure, which may come from some internal and external factors. Such systems can be modeled by Markovian jump systems. The Markovian jump systems possess several operation modes. The switching between the modes is governed by a Markov process. For a fixed operation mode, the evolution of the system is described by a stochastic dynamical system. On the other hand, the phenomenon of impulses exists widely in many evolutionary processes of dynamical systems. A dynamical system could be stabilized or destabilized by certain impulsive inputs. Therefore, it is of great significance to analyze quantitatively the effects of impulses on stability of Markovian jump stochastic systems. In this thesis, the problems of exponential stability in mean square and stochastic finite-time stability of Markovian jump stochastic systems are studied, and some stability criteria are presented. The main contents are stated as follows:(1) The problem of mean square exponential stability of linear Markovian jump stochastic impulsive systems with parametric uncertainty is studied. By taking into account the Markovian jump characteristic of system structure and the discontinuous characteristic of system state, a discontinuous stochastic Lyapunov function is introduced to establish the sufficient condition of exponential stability in mean square with the aid of lto differential formula. Furthermore, using Schur complement and the technique of convex combination, the derived stability condition is formulated into a set of linear matrix inequalities. Numerical simulations show that the stability result derived in this thesis is less conservative than the previous ones.(2) The problems of stochastic finite-time stability and stochastic finite-time stabilization of a class of nonlinear Markovian jump stochastic impulsive systems are studied. Firstly, for a given finite-time interval, by applying the discontinuous stochastic Lyapunov function method, a criterion for stochastic finite-time stability is derived in terms of linear matrix inequalities. Secondly, based on the newly-obtained stability criterion, a sufficient condition for the existence of mode-dependent hybrid state feedback controllers is presented. The gain matrices of the controllers can be achieved by solving a set of LMIs. As byproducts, the design criteria for mode-independent hybrid state feedback controllers, mode-dependent continuous-time state feedback controllers, mode-independent continuous-time state feedback controllers, and impulsive state feedback controllers are also provided. The performance of the above different types of state feedback controllers are compared through numerical simulations.
Keywords/Search Tags:Markovian systems, impulsive systems, stochastic systems, exponential stability in mean square, stochastic finite-time stability, stochasticfinite-time stabilization
PDF Full Text Request
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