Exponential stability for a class of set dynamic equations on time scales

Abstract

Abstract We first present a new definition for some form of exponential stability of solutions, including H-exponential stability, H-exponentially asymptotic stability, H-uniformly exponential stability, and H-uniformly exponentially asymptotic stability for a class of set dynamic equations on time scales. Employing Lyapunov-like functions on time scales, we provide the sufficient conditions for the exponential stability of the trivial solution for such set dynamic equations.

Keywords

• Time scales
• Matrix-valued Lyapunov functions
• Set dynamic equations
• Exponential stability