Consistent Lyapunov methodology: Non-differentiable nonlinear systems (Q2755699)

The paper broadens the classical Lyapunov stability theory by studying the uniform asymptotic stability of invariant sets of time-varying non-differentiable systems. First, the notations used are introduced. Next, the relaxed smoothness properties of the systems are explained and various stability domains are defined. Two functional families \(L(\cdot)\) and \(E(\cdot)\) are used to separate the problem of existence of solutions of suitable differential equations from the stability problem. The main result is a new criteria for asymptotic stability domains of invariant sets. Analogous result for uniform asymptotic stability of invariant sets is also obtained.