Stability Analysis Of Time-delay Systems With Impulsive Input Saturation

Impulsive phenomenon is common in life,with the improvement and development of control theory,impulsive control has now been widely used in the actual engineering control,has become an important means to maintain the stability of the system.At the same time,actuator saturation and time-delay are common factors that affect system stability,their presence often causes degradation of system performance or even affects the stability of the system.Past studies of time-delay systems often do not consider about actuator saturation,and studies on the stability of time-delay systems with implusive input saturation are more complex and less well researched.Therefore,it is of practical significance and theoretical value to further study saturated impulsive control in time-delay systems with respect to stability.The main work of this paper includes the following two aspects.(1)The stability problem of a time-delay switched system with impulsive input saturation is studied.There are more studies on time-delay systems in the previous literature,but there are still relatively few studies on the simultaneous existence of switched and time-delay,less research has been done on saturated impulsive control for such systems.In this paper,we propose a model of time-delay switched system with saturated impulsive input and analyze the stability of the model.The conditions to make the system stable are obtained by combining Lyapunov stability theorem,impulsive differential equation,and convex analysis.Finally,the correctness of the theory is verified by numerical simulation.(2)The stability of a time-delay coupled neural network with impulsive input saturation is studied.Previous literature has studied the stability of pluse coupled neural network(PCNN)more,but less for those with saturation and time-delay factors.In this paper,a time-delay coupled neural network model with impulsive input saturation is constructed.Some LMIs conditions are obtained by constructing suitable Lyapunov functions to ensure its stability under fully impulsive input saturation and partially impulsive input saturation.The correctness of the theoretical analysis is verified by numerical simulations.