Switched Systems With Feedback Control, Time Delay Based On Lmi

Switching systems are a special class of hybrid systems, which contain both a series of continuous and discrete subsystems, and a set of switching rules among subsystems. Current research into switched systems includes system stability analysis, ensuring stability of the system controller and switching rate's design. The dissertation devotes on the study of the feedback control problems of switched systems with time-delay, and the contributions presented in this dissertation can be mainly summarized as the following two aspects:Controllable stability for a class of linear switched systems with time-delay are presented, and also the controller design and the problem of pole location are given. First, non-delay dependent stability of such delay systems is investigated. By constructing a different Lyapunov function of the public system, two types of non-delay-dependent stability conditions and design of the corresponding controller are given. Stability conditions of the first system to control is formulated in the form of the matrix controlled, and by using schur complement theorem, the nonlinear term appearing in the diagonal of control matrix for this conditions is simplified, which is favorable for numerical calculation. The concept of scaling factor is introduced into the second conditions. The principle is to weaken the impact on system stability caused by the system's time-delay, and the corresponding simulation results show that appropriately adjusting the scaling coefficient interval can effectively reduce the impact on system stability caused by the time delay fluctuations. Meanwhile, simulation results also show that when the scaling coefficientεvalues in different regions, the system stability and levels of convergence will be different.Secondly, the delay-dependent stability of such delay systems is researched. Two types of sufficient conditions for the delay-dependent stability of switched systems and the corresponding controller design are expressed. The two conditions are based on the same common Lyapunov function method. But in the first class the nonlinear terms appear in non-diagonal term, which is not conducive to the realization of LMI in the simulation, the second condition improves the first category results, introducing a zero vector, and simplifies non-diagonal nonlinear terms. Numerical examples are given to illustrate the given conclusion.Finally, such linear systems'pole location is investigated. Sufficient conditions of the extreme regional allocation are given to assure the system's pole located in the range of ( -∞,-α).Based on the above research, this dissertation also give research in the delay-dependent stability, controllable conditions, and the regional pole assignment problem of time-delay switched systems with a class of time-delay control input. First, using public Lyapunov functions and LMI inequality, stable conditions for two types of such systems depending on the control input time-delay under arbitrary switching rules are obtained, and the corresponding controller design is given. Secondly, time-delay systems pole assignment problem of such a delay control input is also researched, and sufficient conditions of the extreme regional allocation are obtained to assure the system's pole located in the range of ( -β,-α). Finally, the conclusions given are verified.