State-Dependent Switching Control for Nonlinear Impulsive Switched Systems With Dwell Time
Dan Yang, Xiaodi Li, Guofeng Zhang, Joseph H. W. Lee · IEEE Transactions on Automation Science and Engineering · 2025
This paper investigates the problem of globally exponential stability (GES) for impulsive switched systems via a hybrid switching strategy. First, a switching law combining state-dependent and time-dependent (dwell time) switching strategies is presented in the framework of impulse action. On the basis of the switching law, some GES criteria are proposed by using multiple Lyapunov function technique. A potential relationship among system parameters, impulse action including impulse amplitude and impulse frequency, and the combined switching law is established, which is of vital importance to achieving GES. In addition, when the impulse action involved in switched system is given in terms of stabilizing impulse, the impulsive controller including impulsive gains and impulsive frequency can be designed with the help of the proposed switching law to guarantee the stability of the addressed system. Finally, a simulation example is demonstrated to verify the validity of the proposed switching law and corresponding results. Note to Practitioners—This paper is motivated by the control problem of hybrid systems under a discontinuous environment in practical terms, such as optimal control models in economics, motor controllers in electric vehicles, and traffic flow control in intelligent transportation systems. Due to the hybrid nature of switched systems, they are challenging to compare independently with continuous or discrete systems. Therefore, this paper thoroughly investigates the stability control of nonlinear switched systems in the framework of impulse action. State-dependent switching strategy is an effective control method for on-demand switching. However, existing results often require continuous monitoring of system states, leading to significant computational and communication resource consumption. To address this issue, a hybrid switching strategy including state-dependent and time-dependent switching is firstly proposed for impulsive switched systems in this paper. A relationship among system parameters, impulse action, and the combined switching law is established. Then easy-checked exponential stability criteria are presented based on the proposed hybrid switching strategy. The results demonstrate that the use of hybrid switching strategy significantly reduces switching frequencies and saves control costs while ensuring system stability. In future work, we will consider to explore the application of this novel and efficient switching strategy to study the finite-time stability of hybrid systems, particularly in the presence of inevitable external uncertainties in practical environments.