Research On Impulsive Control And Synchronization Of A Class Of Nonlinear Systems

The concept of impulsive control has been presented since 1999. This control method was paid more and more attention in the current research due to its advanced characteristics and potential applications. In recent years, impulsive control method was used in many system models, and a mass of result was published. Impulsive control was a hot topic in research field of control method.Impulsive control is not a continuous control approach. The main idea of the impulsive control approach is to change instantaneously the state variables of the plant whenever certain conditions are satisfied. The main contributions of this paper are as follows.Firstly, in order to achieve stabilization of a class of nonlinear system, the impulsive control approach is investigated. Based on impulsive differential equations and Lyapunov-like stability theory, sufficient condition is derived to guarantee system stabilization. Numerical simulations are given to illustrate and visualize the effectiveness and feasibility of the theoretical results.Secondly, considering mechanical limitation or device restriction in practical application, impulsive stabilization of nonlinear systems with impulsive gain error is investigated. Compared with the existing impulsive analytical approaches, the proposed impulsive control method is more practically applicable, which includes control gain error with an acceptable boundary. Sufficient condition for global exponential stability of impulsive control systems is obtained, which relaxes the condition for precise impulsive gain efficiently.Finally, in order to solve the leader-following consensus problem of a class of multi-agent system, impulsive consensus protocols is derived. The communication topology can be connected or disconnected, which includes very variety of graph topologies. Some sufficient conditions are obtained to guarantee the states of followers converge to the state of leader asymptotically. Compared with the existing methods, the distributed impulsive controller does not need continuous information, which avoids higher requirements of senor and communication technology.