ISS-equilibrium with stability analysis for disturbed game-based impulsive systems

Abstract

This paper focuses on a class of two-player differential games subject to exogenous disturbances, where one player employs piecewise-continuous control, and the other uses impulsive control. Particularly, the exploration of equilibrium solution in differential games is accompanied by the stability performance analysis of relevant system. To be more specific, the construction of saddle point in zero-sum differential game and Nash equilibrium in nonzero-sum differential game is established under the Lyapunov criteria for input-to-state stability (ISS). Furthermore, owing to the existence of external disturbances and the characterization of ISS property, two extended equilibrium solution concepts are introduced. We propose the definition of $ϵ$-ISS saddle point and $ϵ$-ISS Nash equilibrium for which the corresponding verification theorems are formulated. Finally, two numerical experiments are provided to illustrate the proposed results.