Stability Analysis For Several Classes Of Nonlinear Impulsive Control Systems With Actuator Saturation

The theory of impulsive control is ubiquitous in many practical control systems,and impulsive control has become an important control method for maintaining system stability due to its unique advantages of easy implementation and low cost.At the same time,actuator saturation is a typical constraints phenomenon.The characteristic of actuator saturation is non-smooth,so the dynamic performance of the system will be seriously degraded and the stability of the system will be destroyed.At present,the theoretical research on anti-windup impulsive control is just beginning.Therefore,it is of great theoretical value and potential application significance to study the theory of impulsive control systems with actuator saturation in depth.Based on the existing impulsive system theory and saturation control system theory,this paper deeply studies the dynamic behavior of impulsive nonlinear systems subject to actuator saturation,and proposes the local stability criteria and designs an optimization estimation algorithm of attraction domain.The main contributions and innovations of this paper are as follows:A new hybrid control strategy is designed,which consists of sampled-data controller and impulsive controller subject to actuator saturation.At the same time,we deal with actuator saturation terms by using two different saturation control system analysis methods(convex combination method and sector nonlinearity model approach).Based on the analysis techniques of two different saturation control systems and with the help of Lyapunov stability theory and impulsive control theory,the exponential stabilization of a class of neural network models with input constraints is discussed.At the same time,the effective LMIs conditions are obtained to guarantee exponential stabilization of the considered system,and the attraction domain is estimated.The exponential stabilization problem of nonlinear coupled systems with input constraints is investigated.Two types of hybrid controllers are designed,namely,sampleddata controller and impulsive controller with full input constraints,and sampled-data controller and impulsive controller with partial input constraints.For these two types of hybrid controllers,we consider three cases: firstly,the sampled-data controller and impulsive controller subject to actuator saturation are both beneficial to the stability of the coupled system;secondly,when impulsive controller subject to actuator saturation destroy the dynamical behavior of the coupled system,then the sampled-data controller can be used to ensure the stability of the coupled system;thirdly,when the sampled-data controller can not guarantee the stability of the system,then the impulsive controller subject to actuator saturation will be helpful for the stability of the coupled system.By using the convex combination method and the 2-norm analysis method,the sufficient conditions are established for ensuring the stability of the nonlinear coupled system,and the attraction domain is estimated.The asymptotic synchronization problem of inertial neural networks with unbounded time delay and actuator saturation under impulsive control is considered.A novel impulse differential inequality is established,which can effectively avoid the difficulties caused by unbounded delay and impulsive effects term.By applying the convex combination method,the saturation term in the impulsive controller subject to actuator saturation can be effectively expressed as a convex hull form of several feedback control.And less conservative criteria that guarantee asymptotic synchronization are obtained.As a practical application,a new image encryption algorithm is proposed to utilize the synchronization theory of saturating impulsive control,which can prevent differential attacks.In addition,the validity of new image encryption algorithm can be obtained by experiments.The impulsive stabilization of nonlinear time-delay systems with actuator saturation is studied.By applying delayed-dependent Lyapunov-Krasovskii functional approach,a new series of less conservative linear matrix inequalities criteria are obtained to guarantee the stability of the established systems.The delayed-dependent polytopic technique is able to estimate a larger attraction domain,and this technique is expressed as a convex combination of the product of delay-dependent state vectors and auxiliary matrices.As an application,asymptotic synchronization of delayed inertial neural networks with saturating impulsive control is developed via delay-dependent polytopic technique and delayed-dependent Lyapunov-Krasovskii functional approach.