| Due to impulsive control is easy to implement and less consuming,the theory of impulsive control system has received researchers’ extensive attention.Currently,the most existing results have been focused on studying fixed-time impulsive systems,and a great deal of theoretical and applied results have been obtained.However,in real problems,the impulses of many systems do not occur at fixed time,for example,population control systems,saving rates control systems,ecological systems,some circuit control systems and so on.These types of systems are called state-dependent impulsive systems.Based on the B-equivalence method,the thesis studies the state-dependent impulsive control and synchronization for several classes of nonlinear systems.Based on the state-dependent impulsive control,we study the impulsive control and synchronization of coupled memristive chaotic circuits,the impulsive control and synchronization of complex dynamical networks with nonlinear coupling,the stability analysis of TS fuzzy model for nonlinear systems and state-dependent impulsive control the synchronization for TS fuzzy memristive chaotic systems with parameter mismatches.The main contents and contributions of this thesis are as follows:1.The control and synchronization of coupled memristive chaotic circuits with statedependent impulsive control.Based on the state-dependent impulsive control,we first study the impulsive stabilization of the memristive chaos circuit.Then by using B-equivalent method,the statedependent impulsive synchronization of two memristive chaos circuits is investigated.One of the memristive chaos circuits is considered as the driving system,the state variables of the driving system(driving system which does not involve the impulses)are transmitted to the response system and then the state variables of response system are subjected to jumps at the state-dependent impulsive instants,and ultimately to achieve synchronization.Establishing several assumptions,the error system with state-dependent impulses can be reduced to the case of fixed-time impulses,and the Lyapunov function analysis method is used to obtain the global exponential stability criterion of the error system.2.The state-dependent impulsive control and synchronization of complex dynamical networks with nonlinear coupling.First,without adding impulsive controller,only with the feedback controller,the fixed-time consensus problem for complex dynamical networks with nonlinear coupling is study.Then,the concept of state-dependent impulsive control is introduced into the complex dynamics network model,the local asymptotic and global asymptotic synchronization problem for complex dynamics networks with state-dependent impulses is investigated.By using the B-equivalent method,the state-dependent impulsively controlled synchronization error nodes for complex dynamical networks can be reduced to fixed-time impulsive error system.By applying mathematical induction,the sufficient conditions of the stability criterion for the reduced error system can be obtained.The validity of the theoretical results was verified by two numerical simulations.3.The stability analysis of TS fuzzy system with state-dependent impulsesIn order to control the TS fuzzy system effectively,the state-dependent impulsive controller is added into the system,and then study the stability of the TS fuzzy system with state-dependent impulses.Several assumptions are established to ensure that each solution of the system intersects the discontinuity exactly once.Using the B-equivalence method,the state-dependent impulsive TS fuzzy system can be reduced to a fixed-time impulsive TS fuzzy system.By applying comparison theorem,the comparison system of the fixed-time impulsive TS fuzzy system can be obtained,then analyze the stability of the comparison system.The numerical examples are carried out to demonstrate that the stability properties of corresponding fixed-time impulsive systems imply the same stability properties of the considered state-dependent impulsive control systems,and finally establish a set of stability criteria by use of comparison system.4.The impulsive Synchronization for TS Fuzzy Model of Memristive Chaotic Systems with Parameter MismatchesUsing the singleton fuzzifier,fuzzy inference and a weighted average defuzzifier,the TS fuzzy model of memristive chaotic system is constructed.The state-dependent impulsive control synchronization problem of the model with parameter mismatches is investigated.Using the B-equivalent method,the state-dependent impulsive TS fuzzy error system with parameter mismatch can be reduced to the case of fixed-time impulses.Furthermore,using the linear decomposition and comparison methods,the stability conditions of the fixed-time impulsive error system are obtained.Finally,the numerical simulation results are presented to illustrate the effectiveness of the theoretical results. |
