Research On Stability And Stabilization Of Nonlinear Systems Via Periodically Intermittent Control

Periodically intermittent control is a discontinuous control which bridges the gap between continuous feedback control and impulsive control. In com-parison with the continuous feedback control, intermittent feedback can ef-fectively reduce control cost. On the other hand, compared with impulsive control, intermittent feedback can lead to better control performance. In re-cent years, the periodically intermittent control strategy has been broadly ap-plied to synchronize and stabilize the nonlinear systems, and many important results have been achieved. However, most of these stability results were established by time-invariant Lyapunov function/functional based methods. The deficiencies of the current research are mainly reflected in the following two aspects:1) the achieved stability results are not suitable for intermittent controllers design; 2) these stability results cannot be used to solve the in-termittent stabilization problem for the systems with unknown delays. Faced with these problems, in this thesis, piecewise Lyapunov function/functional based methods have been proposed to reduce the conservatism entailed in the current time-invariant Lyapunov approach, weaken the restriction on the sizes of time-delays, and solved the synthesis problem of intermittent controllers. The main results derived in this thesis are listed as follows:(1) The problem of periodically intermittent stabilization of a class of continuous-time nonlinear system is studied. A piecewise time-dependent Lyapunov function based analysis method is proposed. By applying this method, a new sufficient condition is derived in terms of linear matrix in-equalities. A criterion for designing state feedback intermittent controllers is also presented. Compared with the previous results, the control width ensur-ing stability is reduced.(2) The problem of periodically intermittent stabilization of delayed neural networks for the case where the time-delay may be restricted is s-tudied. Under the assumption that the time-delay is less than the control width, two types of piecewise Lyapunov function/functional based analysis methods with respect to the types of state delays are presented. Based on the established stability results, several criteria for designing intermittent control gain matrices are provided. Both theoretical analysis and numerical examples have demonstrated that the derived results improve the existing ones.(3) The problem of periodically intermittent stabilization of delayed neural networks for the case where the time-delay may be greater than the control width is studied. By introducing exponential-type piecewise Lya-punov functions/functionals, the restriction that the time-delay must be less than the control width is removed. For the case where the time-delay is slowly-varying, by introducing a new type of piecewise time-dependent Lya-punov functional, for the first time, a stability criterion which can guarantee the periodically intermittently controlled system to be exponentially stable irrespective of the size of time delay is achieved. Some design methods for optimizing the norms of the intermittent control gain matrices are presented.(4) The problems of periodically intermittent stabilization of a class of discrete-time nonlinear systems and a class of discrete-time nonlinear delay systems are studied. By applying discrete-type piecewise Lyapunov func-tion/functional analysis techniques, several criteria for exponential stability of the periodically intermittent controlled systems are obtained. Furthermore, the state feedback intermittent controllers can be designed in terms of the fea-sible solutions to a set of linear matrix inequalities.