Controller Design And Stability Analysis For Dynamic Systems Based On Sliding Mode Surfaces

With the rapid development of science and technology and the improved arith-metic ability of human,a lot of experts and scholars are interested in automatic control,which can promote the development of the military,aerospace industry,people's livelihood and so on.In fact,there must be external disturbances and un-certainties in the models of actual systems.All these factors can be settled by sliding mode control(SMC).So lots of experts pay attention to it.SMC is with the fast response speed and the strong robustness to external disturbances and uncertainties of the system,which is favored by scholars.Due to delay and“noisy" almost being common factors in most models,Markovian jump systems presenting the stochastic switching in the real world more precisely,T-S fuzzy models approximating a class of nonlinear system more effectively,based on SMC,this dissertation proposed new cri-teria and methods for some dynamic systems.The main contents and contributions are listed as follows:(1)The stability analysis and controller design of delayed linear systems with mismatched uncertainties are studied.Firstly,an adaptive integral sliding mode control is given to guarantee the sliding mode reaching condition in finite time with the upper bound of external disturbance unknown.Secondly,we give a lemma.By this lemma,a delay-dependent sufficient condition is presented by means of linear matrix inequalities(LMIs)which makes sliding mode dynamics asymptotically stable.Lastly,in order to reduce the conservativeness of the obtained stability condition,we present a new sufficient condition by means of delay-time partitioning approach.The maximum delay guaranteeing the stability of the system could be obtained through this method.(2)The stabilization problem for a class of uncertain Markovian jump system with time-delay and matched external disturbance is studied with jumping transfer matrix unknown,partly unknown,or known.Firstly,a new integral sliding mode surface named stochastic sliding surface(SSS)is introduced.The SSS is characterized that the state trajectories are on the sliding surface all the time even at the time of system switching.So the problem of the state trajecto-ries moving among several sliding surfaces by use of traditional sliding mode control method is settled perfectly.Secondly,sliding mode control(SMC)law is synthesized to avoid the state trajectories escaping from the surface.Last-ly,based on SSS,the stability criteria(LMIs)of sliding mode dynamics are derived with the jumping transfer matrix unknown,partly unknown or known.(3)The stabilization problems for a class of singular Markovian jump system with Brownian motion is studied with jumping transfer matrix unknown,partly unknown,or known.Firstly,the problem of reaching sliding mode surface is settled by use of SSS when system switches.Secondly,due to the two dificul-ties(1 There exists square term of the considered system state in control law,at the same time,the considered system is singular one.Thus,there is not a unique solution;2 There is a s/?s?2 term in control law where s represents the sliding surface function.It can deduce the control law infinite.)caused by use of traditional Lyapunov method,a new stability criterion of reaching law is proposed by improved Lyapunov method,which can avoid the two difficulties.And the control law deduced by the new criterion can keep the system on the sliding surface and not escaping from the surface.Last,the stability criteri:a(LMIs)of sliding mode dynamics with different cases in jumping transfer matrix are provided.(4)The robust stabilization of fuzzy singular systems with time delay and fuzzy stochastic singular systems is investigated.Firstly,a new sliding surface named vector integral sliding mode surfaces(VISMS)is proposed.Fuzzy system with different input matrices can be stabilized by the proposed surface.Secondly,a lemma is given to judge what kind of systems can be stabilized.In other words,it could be judged whether the considered system can reach the new surface or not.Then,a sliding mode control law is proposed according to VISMS.It can make the considered system reach the VISMS and keep on it thereafter.When the system is stochastic one,a new stability criterion is proposed by improved Lyapunov method to avoid the difficulty caused by stochastic singular systems.Lastly,the stability criteria(LMIs)of sliding mode dynamics are provided.