Practical exponential stability of perturbed triangular systems and a separation principle

State feedback control law for a class of nonlinear time-varying system under unknown time-varying delay

“…Many researches have devoted themselves to design effective control approaches to guarantee the system stability [1,5,6,9,12,18,28]. Indeed, in citeHam01, the global stabilization problem for a relatively broad class of nonlinear plants is discussed.…”

Exponential convergence of nonlinear time-varying differential equations

“…It is known that requiring the existence of a Lyapunov function that satisfies certain conditions implies practical exponential stability (see, e.g., [4], [6]- [9]). Requiring the existence of an auxiliary function V (t, x) that satisfies certain conditions is typical in many results obtained by Lyapunov's method.…”

“…This method employs construction of a Lyapunov function. Converse Lyapunov results are an important tool in the analysis of stability of nonlinear time-varying systems and have been well studied (see [4], [10] - [12]). …”

“…The purpose of this paper is to obtain a converse Lyapunov theorem for uniform global practical exponential stability. In our proof of this result we use some arguments from [4,10].…”

On The Practical Stabilization of Dynamical Systems With Application

“…In the next section we present some definitions and preliminary results necessary to state our main theorems. In section 3, we present our main results: First, we propose new sufficient conditions using the extended Lyapunov functions for the practical exponential stabilization of nonlinear time-varying systems (1) and (2) with control. Second, we give an illustrative example to show the applicability of the main result.…”