Tube-based Control And Filtering Of Switched Systems

As the advantages become visible gradually,the switched models and switched control strategies have been widely employed in a lot of practical systems such as gearbox transmission control systems,power converter systems,networked control systems,short take-off and landing aircrafts and activated sludge waste water process systems.From the theoretical aspect,attentions of researchers have been focused on the control problem and filtering problem.Typically,advanced techniques have been proposed via two approaches: The first one is to view the considered problem in micro level instead of macro level such that problems which are difficult or even unable to be solved at macro level can be solved easily.However,the difficulty of utilizing this approach is how to split the considered problem into pieces properly.The other approach is to relax the assumptions that is required when modeling a switched system such that the new assumption can be as close as the practical system.This is helpful for analyzing the performance of the practical system.Generally speaking,a novel proposed technique,which is helpful for improving the system performance,can only be suitable for some certain cases and it is not easy to be extended to others,especially for switched systems.In other words,the use of many existing techniques proposed in literature are significantly constrained.Moreover,the assumptions when modeling the switched system are relatively tight.Therefore,two meaningful works raised recently: to extend the existing techniques to a wider range of systems and to relax the assumptions such that the analysis and synthesis approaches of switched systems can be more effectiveness.This thesis is focused on developing the control and filtering theory for switched systems in this two aspects.The main contents can be summarized as follows:The observer-based robust stabilization problem of a class of modal average dwell time?MADT?switched system whose states are only partially measurable is considered.It is worth noticing that the related results published in literature are with conservatism.The quasi-time-dependent technique is useful in reducing the conservatism of controller design.However,the technique is only suitable for dwell time?DT?switching case or persistent dwell time?PDT?switching case,the existing results cannot be used for MADT switched system directly since continuous switchings is allowed at arbitrary admissible time intervals and it is hard to determine the length of each time interval of continuous switchings.Hence,in this paper,some amendments have been made for quasi-timedependent technique such that it can be employed to solve the stabilization problem of MADT switched system.With the help of linear copositive Lyapunov function,the stability of the considered system has been investigated.On the basis of the stability result,observer-based stabilization controllers,both for single-input systems and multi-input systems,have been designed with less conservatism.Moreover,with the existence of switching detection delay,the quasi-time-dependent technique has been utilized to reduce the conservatism of asynchronous filter design of switched systems by making amendments on the asynchronous switching rules among sub-filters.On the basis of the conservatism of robust filter of switched positive system has been reduced by employing the quasi-time-dependent technique,the technique for improving the filtering accuracy have been investigated.The filters that can estimate the boundaries of the actual trajectory of the output are designed firstly.Next,a novel weighted-average technique is proposed to reduce the filtering error.The selection of weights has been discussed in detail and the worst ?₁-gain performance of an arbitrary admissible weight has been analyzed.The new proposed weighted-average technique is practicable and has satisfactory filtering error.The asynchronous controller design and the asynchronous filter design of switched systems with overlapped detection delay are investigated.The structure of overlapped detection delay has been discussed in detail firstly as well as a novel approach has been proposed to clarify the different time intervals of the closed-loop system.For switched systems with DT and modal DT?MDT?,a novel two-stage Lyapunov function,by which the time interval between any two consecutive switchings is divided into two stages such that the energy function for the first stage can be focused on converging while converging when the system working on synchronous status and diverging not to fast when the system working on asynchronous status at the second stage,is proposed to analyze the stability of the filtering error system.Next,the robust stability criteria have been established for the two kind of switched systems with energy-bounded additive disturbance.Through which,the H_? stabilization controller and the ?₁ positive filter are designed.The disturbances exists in practical systems are persistent and amplitude-bounded is considered.In such a case,the robust control strategies are unavailable.Hence,the tubebased control strategy is considered for switched systems with ADT.Firstly,the attention is concerned with the computation of robust positive invariant?RPI?set for switched systems with ADT.To this end,the switching signal is divided into stages with constant length by a sequence-based technique such that all the possible switching sequences in each stage can be exhausted.Hereafter,the existence of the a RPI set has been established as well as the explicit computation algorithm has been designed.In order to reduce the computational burden of the explicit computation algorithm,two approximate algorithms have been proposed alternatively.For facilitating the employment of the obtained RPI set,some characteristics have been exploited subsequently.Combining with the standard robust control results,a dynamic tube is designed such that the system states converge to the tube and then enter the tube periodically since the first time it happened.Upon proposing the tube-based controller of switched system with ADT,the error constrained tube-based state estimation problem is investigated.The disturbances taken into considered is also persistent and amplitude-bounded.The estimation error is constrained by a polytope set.In order to obtain necessary tools for solving tube-based state estimation problem,the computations of maximum constrained admissible contractive set?with given contractive factor?and maximum constrained admissible invariant set of ADT switched system are investigated firstly.A more general division technique of switching signal,which includes both the technique employed in literature for DT switched system and the sequence-based technique proposed in early this paper,is proposed.The novel division technique not only allows different lengths for different stages but also allows switching appears in any stage.Hence,according to the definition of ADT switching signal,in a stage with finite length,the admissible switching sequence can be exhausted.Moreover,if the lengths of stages take values in a finite set,all the admissible switching sequence for all stages also can be exhausted.In such a case,the existence of constrained admissible contractive set and constrained admissible invariant set are established.The backward iteration algorithms is employed to compute the two sets.The two computation algorithms are explicit and can be terminated in finite steps.Based on the two sets obtained,a dynamic contractive tube and a dynamic invariant tube are constructed for the considered systems respectively.As for the former?latter?,the actual system state initialed from the tube will enter a smaller one?the same one?periodically.Moreover,the estimation error satisfies the set constraint at all time.