Hybrid Impulsive Control For Several Classes Of Uncertain Singular Markovian Jump Systems

In recent years,much attention has been paid to singular Markovian jump systems.Compared with normal systems,singular Markovian jump systems are more complicat-ed,in which the regularity,impulse elimination or causality,consistent initial condition and stability should be considered simultaneously.In particular,when the derivative ma-trices of singular Markovian jump systems have uncertainties,the control problem will become more difficult.Given the impact of time-varying uncertainties and stochastic switching,an impulsive and proportional-derivative control strategy is presented to deal with the problem of robust normalization and hybrid impulsive control for several classes of uncertain singular Markovian jump systems.Main results are summarized as follows.(1)The problem of robust normalization and guaranteed cost control is investigated for uncertain singular Markovian jump systems via hybrid impulsive control.The uncer-tainties exist in both system matrices and transition rate matrix of the Markov chain.An impulsive and proportional-derivative state feedback controller is proposed,by which the resultant closed-loop system over all admissible uncertainties is normal and robustly s-tochastically stable with a minimal upper bound of the cost function.Based on Lyapunov theory,congruence transformation and free-weighting matrix technique,a sufficient con-dition for the existence of guaranteed cost controller is obtained and the expression of de-sired controller is also given.The cost function is minimized via solving an optimization problem under the designed control scheme.The gain matrices of the impulsive control part are parameter variables,which can be solved together with the design approach.This can provide more design freedom and reduce the conservatism to a certain level.(2)The problem of robust normalization and strictly(Q,S,R)-dissipative control is investigated for uncertain singular Markovian jump systems via hybrid impulsive con-trol.The uncertainties exist in derivative,state,input matrices and transition rate matrix of the Markov chain.An impulsive and proportional-derivative state feedback controller is proposed,by which the resultant closed-loop system over all admissible uncertainties is normal,robustly stochastically stable and strictly(Q,S,R)-dissipative.Based on s-tochastic Lyapunov function,slack matrix and matrix inequality technique,a sufficient condition for the existence of strictly(Q,S,R)-dissipative controller is obtained and the explicit desired impulsive and proportional-derivative state feedback controller is also given.Moreover,the dissipative control results provide a unified framework of H? con-trol and passive control.The derivative feedback and impulsive feedback are parameter variables to be solved together with the design approach,which can provide more design freedom.(3)The problem of robust normalization and reliable dissipative control is investi-gated for uncertain nonlinear singular Markovian jump systems via hybrid impulsive con-trol.An impulsive and proportional-derivative state feedback controller is proposed,by which the resultant closed-loop system over all admissible uncertainties is normal,robust-ly stochastically stable and strictly(Q,S,R)-dissipative in the case of actuator failures.Based on fault tolerant technique and linearization approach,a sufficient condition for the existence of reliable dissipative controller is obtained.According to congruence trans-formation,free-weighting matrix and matrix inequality technique,the explicit desired impulsive and proportional-derivative state feedback controller is also given.Moreover,the dissipative control results include H? performance and passive control as special cas-es.The derivative feedback and impulsive feedback are parameter variables to be solved together with the design approach,by which better performances can be achieved for the resulting closed-loop system.(4)The problem of robust normalization and H? control is investigated for uncer-tain time-delay singular Markovian jump systems via hybrid impulsive control.Norm-bounded parameter uncertainties exist in derivative,state and input matrices.An impul-sive and proportional-derivative state feedback control strategy with memory is present-ed,by which the resultant closed-loop system over all admissible uncertainties is nor?mal,robustly stochastically stable with H? performance.Based on stochastic Lyapunov-Krasovskii function,congruence transformation and matrix inequality technique,a suffi-cient condition for the existence of impulsive and proportional-derivative memory state feedback controller is obtained and the expression of desired controller is also given.Delay-dependent results are given in terms of linear matrix inequalities,which are flexi-ble and applicable.(5)The problem of robust normalization and H? control is investigated for uncertain time-delay nonlinear singular Markovian jump systems via disordered control.Subjec-t to packet disordering during the transmission process,the operation modes of resul-tant closed-loop system are associated with both the original operation modes of system matrices and the new operation modes of control gains.By adopting differential mean value theorem,stochastic Lyapunov-Krasovskii function and convexity principle,a suffi-cient condition for the existence of H? disordered controller is obtained.Based on the framework of probability theory and non-fragile control method,a hybrid impulsive con-troller only related to the original operation modes is constructed in terms of stationary distribution.The resultant closed-loop system is still robustly stochastically stable with disturbance attenuation performance,even if the signal of operation modes is out of order during the transmission process.Finally,the results of the dissertation are summarized and further research topics are pointed out.