Finite-Time Stability Analysis And Synthesis Of Discrete-Time Markov Jump Systems

Markov jump systems have received considerable attention in the last decades owing to their competence to model the unexpected changes of dynamic systems.The transition probabilities of Markov jump systems in the most results are assumed to be time invariant.However,the existence of various unfavorable factors in practical applications leads to the time-varying transition probabilities.On the other hand,due to the advantage to reflect the transient performance of dynamic systems during a finite-time interval,finite-time stability plays a key role in many engineering applications,such as robots,unmanned aerial vehicles,biochemical reaction s and so on.Based on the above discussion,this thesis considers the finite-time H_? filtering and control problems for discrete-time Markov jump systems with time-varying transition probabilities,missing measurements,parameter uncertainties,and communication constraints.The main results are obtained as follows.1.For the discrete-time Markov jump systems,the stochastic phenomenon of missing measurements and time-varying transition probabilities are considered.The time-varying transition probabilities are assumed to be finite piecewise homogenous and the missing measurement phenomenon is modelled as a Bernoulli distributed sequence.Based on an H_? filter,sufficient conditions of finite-time boundedness for the filtering error system are established,and the filter gains are obtained.A numerical example is presented to demonstrate the applicability of the obtained results.2.For the discrete-time Markov jump systems,the time-varying transition probabilities are modelled as convex polyhedron.A Luenberger observer is designed to measure the system state.By applying a slack matrix,the cross coupling between system matrices and Lyapunov matrices is eliminated.Sufficient conditions of stochastic H_? finite-time boundedness for close-loop systems are derived in light of linear matrix inequalities.3.For the nonhomogeneous discrete-time Markov jump systems with communication constraints,a polytope is applied to describe the time-varying transition probabilities.The burden of communication is reduced by employing a mode-dependent event-triggered strategy.Based on finite-time analysis and linear matrix inequalities techniques,Sufficient conditions of the stochastic finite-time boundedness with H_? performance are obtained for the close-loop systems,and the gains of the filter are designed.