Analysis And Synthesis For Switched Systems With Incomplete Information

In recent years,with the increased automation and the development of information technology,the system structure becomes increasingly complex.The investigation for system with single-system has already been extended into the system with many subsystems.Compared to the research of system with single-system,the investigation for switched systems with multi-subsystem need consider not only the performance of each subsystem,but also switched rules.Consequently,the related studies for switched systems are complex and challenging.On the other hand,with the networks being popular,the accuracy and integrity of the information plays a critical role in the performance of the switched systems.Therefore,it is necessary to further improve the theory of switched systems with incomplete information.Novel ideas and approaches for the stability analysis,the modeling and the effect of the incomplete information are developed in this thesis in order that less conservativeness and more features on network induction phenomenon are implied by the obtained stability criteria.The content of this thesis is mainly divided into three parts.In the first part,we focus on the fault detection,H? filtering and asynchronous switching problems for the piecewise linear(PWL)system,which is commonly used in engineering.In the second part,we consider the control problem for a class of switched systems with known joint distribution function of sojourn time and system mode.Moreover,we study the filtering problem for the switched systems with time-varying sojourn probabilities.In the third part,we further study the application of switching method.We use the switching model to depict the energy allocation for muti-agent systems and large-scale systems.Studying works are listed as follows:1.Some interesting problems are investigated for a class of discrete-time piecewise linear(PWL)systems with external disturbances and infinite distributed time-delays.The first attention in this part is focused on the design of filters such that,under the quantisation effect,the H? performance of the augmented dynamic system is guaranteed with a prescribed attenuation level.Such a technique relies on the forward solution to a set of recursive linear matrix inequalities.Moreover,an appropriate approach of fault detection and filter design problem is provided to achieve a satisfactory balance between the disturbances attenuation level and the sensitivity to the fault for the proposed PWL systems.As a consequence,a sufficient condition is obtained in terms of the linear matrix inequalities such that,for all admissible infinite distributed time-delays and external disturbances,the system is guaranteed to be asymptotically stable and the residual is guaranteed to satisfy H?filtering performance and fault detection performance.2.The H? filtering problem is investigated for PWL systems with incomplete information and partial observable modes.First,a Markov chain with known probability distribution and a filter parameters' storage rule are introduced to overcome the difficulties resulting from Stochastic Access Protocol(SAP)and the partial observable mode information,respectively.Then,by resort to the proposed storage rule,a novel asynchronous H? filter is presented with partial mode information.Subsequently,the filter parameters are obtained by solving a series of probability-dependent linear matrix inequalities.3.A more general switching rule is employed,under which the probability distribution of switching is dependent on both the sojourn time and the system mode.The aim of the problem addressed is to design a quantized controller such that,under the Round-Robin(RR)protocol,the switched system with the known joint distribution is mean-square stable(MSS).Considering the sojourn time and the periodicity of RR protocol,we present an interval-dependent periodic condition to guarantee the stability of addressed systems and then derive the explicit expressions of controller for each subsystem by solving a set of matrix inequalities.4.The co-design strategy of event-triggered scheme and fault detection filter(FDF)is developed for the networked switched systems with delayed measurements.A novel switching rule is proposed to better describe the switching behavior in real system,under which the probability staying in each subsystem is time-varying and results in a piecewise continuous system dynamics.Combining the stochastic analysis techniques and the average dwell time(ADT)method,a sufficient condition is obtained to guarantee the finite-time boundedness of the generated residual system,the sensitivity of the residual signal to faults and the disturbance attenuation of the switched system to external disturbances.Based on the established condition,a co-design strategy is developed to get the event-triggered threshold and the FDF gain.5.In terms of the sojourn probabilities,the probability-dependent finite-horizon consensus control problem is studied for multi-agent systems under the energy constraint.First,a random vector satisfying a certain probability distribution is employed to describe the high energy and low energy allocation.Then,a random variable sequence following the Bernoulli distribution with time-varying probability is employed to describe the data packet dropout.Furthermore,by using the gain-scheduled method based on the time-varying probability of data packet dropout,a sufficient condition is established to guarantee the desired performance of the designed finite-horizon controller with given energy allocation probability.Finally,the gain-scheduling controller for each agent can be obtained in terms of the feasible solutions of a set of linear matrix inequalities.6.By employing average dwell time method,a distributed control problem is investigated for large-scale systems under the RR protocol and energy constraint.The large-scale system powered by a public energy center is decomposed into a number of interconnected subsystems,which are equipped with independent sensor and controller,respectively.An energy allocation scheme is employed,under which each sensor is powered by high energy or low energy to satisfy the energy constraints.When sensors use low energy,packet dropout may occur with a certain probability.Based on the network topology,protocol,energy allocation and induced packet dropout,a novel distributed controller model is established for the lager-scale systems and then the explicit expressions of controller for each subsystem are derived by using recursive design methods,average dwell time(ADT)methods and random statistic methods.