Analysis And Control Design For A Class Of Switched Singular Systems

As a particular class of hybrid systems, switched systems are of great significance in both theoretical value and engineering applications. For the linear switched systems,many efforts have been done to the study of normal switched systems. Compared with normal switched systems, analysis and control design of switched singular systems are more complex and more challenging because of the complexity and regularity of its struc-ture, the elimination of the pulse mode, the state jumps and the initial state, thus, a few research results on switched singular systems are reported and there are still a lot of problems to be solved. In this thesis, we will further study the analysis and control design of switched linear singular systems, the main contributions are as follows:Chapter 1 is the preface, the research background and general situation of this disser-tation are introduced. The research significance, methods and contributions of switched systems, singular systems and switched singular systems also the main work and the structure of this dissertations are briefly introduced.Chapter 2 studies the global exponential stability (GES) analysis for a class of switched linear singular systems under any switching signal with dwell time specifica-tions. Unlike the classical dwell time method, the dwell time is an arbitrarily prespecified constant, which is not computed by Lyapunov functions of the subsystems. Under all of the subsystems are exponential stability, first of all. based on dynamic decomposition technique, convert the problem of stability analysis of switched singular systems into an equivalent one of for reduced-order switched normal systems with state jumps; then, by constructing certain new multiple piecewise time-varying Lyapunov functions, computable sufficient conditions for stability analysis of a class of switched singular systems under d-well time specifications. Finally, the simulation is given to illustrate our obtained stability results are less conservative.Chapter 3 investigates the global stabilization design of a class of switched singu-lar linear systems via a novel mode-dependent dwell-time switching. The distinguishing feature from chapter 2 is that stability of all subsystems of the switched systems is not nec-essarily required. Given the assumed instability of individual subsystems, firstly, based on dynamic decomposition technique, convert the problem of stabilization design of switched singular systems into an equivalent one of for reduced-order switched normal systems with state jumps; secondly, by constructing certain new multiple piecewise time-varying Lya-punov functions, the stabilization of the switched system is achieved under the condition of confining the dwell time by a certain pair of upper and lower bounds, which restrict the growth of Lyapunov function for the actively operating subsystem, thus forcing "energy"of the overall switched system to decrease at the switching instants. Finally, an example is presented to demonstrate the effectiveness of the proposed method.Chapter 4 addresses the problem of finite-time stability for a class of switched linear singular systems under any switching signal with dwell time specifications. First of all,based on dynamic decomposition technique, convert the problem of finite-time stability of switched singular systems into an equivalent one of for reduced-order switched con-ventional systems with state jumps; then,by constructing certain new multiple piecewise time-varying Lyapunov functions, computable sufficient conditions for finite-time stabil-ity of a class of switched singular systems under dwell time specifications. Finally, an example is presented to demonstrate the effectiveness of the proposed method.Chapter 5 investigated and solves the design of adaptive impulsive observers for a class of uncertain switched nonlinear systems with unknown parameter. Sufficient conditions are derived for designing such observers for each subsystem to reconstruct asymptotically and update system states in real time. The state observer is represented in terms of impulsive differential equations. The parameter estimation law is modelled by an impulse-free, time-varying differential equation associated with the impulse time sequence in order to determine when the observer estimated state is updated. The asymp-totic convergence to zero of the observation errors is established by applying the method of multiple time-varying Lyapunov functions. Sufficient conditions are derived that guar-antee the convergence of parameter estimation. An example of switched Lorenz system along with numeric and simulation results is presented to demonstrate the effectiveness of the proposed method.The conclusions and perspectives end the dissertation.