Stabilization of nonlinear dynamical systems via intermittent control with non-instantaneous impulses and actuator saturation

In many actual discontinuous control systems, the state might undergo some abrupt changes when the impulsive effects appear and the impulsive effect will stay active for a period of time which can not be ignored. Obviously, the traditional instantaneous impulsive system models can not describe the above process. Then in this paper, considering the actuator saturation and non-instantaneous impulse existing in the real environment, we formulate the new models to describe the nonlinear intermittent control system subject to actuator saturation with non-instantaneous impulsive effects occurring at the moments of system switching. Some exponential stability criteria of this considered intermittent control systems in the form of matrix inequalities are first put forward. Meanwhile, some LMI optimization problems are also proposed to design the control gain for estimating the attraction domain with a fixed decay rate. Finally, simulation results demonstrate the feasibility of the obtained theoretical results. • The new mathematical models are established to describe the intermittent control with non-instantaneous impulsive effects and actuator saturation. • The intermittent control subject to actuator saturation and non-instantaneous impulsive effects is used to realize the stabilization of a class of nonlinear systems. • Some exponential stability criterion of this intermittent control systems in the form of matrix inequalities are put forward. • In order to design the control gain so as to estimate the attraction domain as large as possible with a fixed decay rate, some optimization problems are put forward.