Stability And Stabilization For Switched Stochastic Nonlinear Systems

Due to the increasing complexity of engineering systems,switched systems have appeared more and more frequently in various engineering applications and have been one of the hot topics in control area.On one hand,the introduction of switching can enhance the performance of the overall systems.However,on the other hand,the existence of switching makes it quite difficult in stability analysis and control synthesis for switched systems.Although,many approaches and techniques have been developed for stability and control of the switched systems,there are still some areas for improvement.For instance,some conditions used to check stability are strict,or the design of controllers is quite complex and hard to implement.Taking into account the fact that many real systems are easily subjected to various random noises,the study of switched stochastic(or random)nonlinear systems has gradually gained more and more researchers' at-tention.Because of the randomness,there are essential differences between switched stochastic systems and switched determinate systems.Hence,the results for determinate systems cannot be used directly to stochastic ones,and many results for switched stochastic nonlinear systems have not been reported in the existing literature.Based on the previous works,stabilization,stochastic dissipativity,stochastic stability are investigated for switched stochastic(or random)nonlinear systems in this thesis.The main work consists of the following aspects.A class of switched stochastic nonlinear systems with stochastic inverse dynamics is inves-tigated.By using backsetpping technique,output-feedback stabilization controller is designed.Because of some states can not be directly measured,a reduced-order observer is introduced.The observation error dynamic can be described by an error switched system.Based on the controller design procedure,an interconnected switched system composed of the error switched system and the coordinate transformed switched system is constructed.With the help of the changing supply rate of stochastic inverse dynamics and stochastic nonlinear small-gain theorem,the stability of the closed-loop switched system is considered.From the view point of energy,dissipativity theory plays an important role in control area.In addition,since many switched systems are easily disturbed by white noise in practice,dissipativi-ty of stochastic nonlinear systems with state-dependent switching is investigated.By introducing stopping times reasonably,state-dependent switching signal is converted into a time-dependent one.Then,the notion of dissipativity and dissipative inequalities for switched stochastic nonlin-ear systems are presented.Based on the dissipativity analysis,some criteria on global asymptotic stability in probability for switched stochastic systems can be obtained by virtue of Lyapunov functions technique and stochastic version of the comparison principle.For many control tasks in engineering,it is more reasonable to describe the final effects of stochastic disturbances by stationary processes than by white noises.To this end,noise-to-state stability(NSS)for random nonlinear systems with second-order processes under state-dependent switching is investigated.With the help of some easily verified conditions and a reasonable estimation for the second-order processes,the criteria on NSS of random switched systems are presented by the aid of Dynkin formula.The reasonability of the obtained results is illustrated by using a double pendulum in random vibration environment.Conventional criteria on Lyapunov stability are based on the negativity of the time deriva-tive or the infinitesimal generator of Lyapunov functions,it is demonstrated that these criteria are conservative.Taking this fact into account,the infinitesimal generator for each active subsystem acting on Lyapunov functions is relaxed to be indefinite with the help of uniformly stable func-tion.Subsequently,improved criteria on asymptotic stability for switched stochastic nonlinear systems are proposed by applying the weakened condition and mode-dependent average dwell time technique.