Exponential-weighted input-to-state stability of hybrid impulsive switched systems

Stability of the non-linear systems with external inputs is an important problem in control theory and engineering. Input-to-state stability (ISS) is one of the stability concepts that have been introduced to non-linear systems. This study extends the ISS to a more general case, namely, exponential-weighted input-to-state stability (e^λt-weighted ISS). By employing the Lyapunov function and Lyapunov-Razumikhin techniques, e^λt-weighted ISS is proposed and studied for the impulsive switched hybrid systems with and without time delay. An example and simulation results are given to illustrate the effectiveness of the obtained theoretical results.