No abstract

Purpose The purpose of this paper is to report on the global practical uniform h-stabilization for certain classes of nonlinear time-varying systems and its application in a separately excited DC motor circuit. Design/methodology/approach Based on Lyapunov theory, the practical h-stabilization result is derived to guarantee practical h-stability and applicated in a separately excited DC motor. Findings A controller is designed and added to the nonlinear time-varying system. The practical h-stability of the nonlinear control systems is guaranteed by applying the appropriate controller based on Lyapunov second method. Another effective controller is also designed for the global practical uniform h-stability on the separately excited DC motor with load. Numerical simulations are demonstrated to verify the effectiveness of the proposed controller scheme. Originality/value The introduced approach is interesting for practical h-stabilization of nonlinear time-varying systems and its application in a separately excited DC motor. The original results generalize well-known fundamental result: practical exponential stabilization for nonlinear time-varying systems.

In this work, we establish some new sufficient conditions to show the uniform h-stability for nonlinear time-varying perturbed systems which can be viewed as an extension of the uniform exponential stability and polynomial stability. Also, we study the boundedness of solutions when the origin is not necessarily an equilibrium point of the perturbed system. The idea is to use some Gronwall type integral inequalities. As an illustration, we present some examples with simulations to show the applicability of the obtained results.

UDC 517.9 We solve the following twofold problem: In the first part, we deduce Lyapunov sufficient conditions for practical uniform exponential stability of nonlinear perturbed systems under  different conditions for the perturbed term. The second part presents a converse Lyapunov theorem for the notion of semiglobal uniform exponential stability for parametrized nonlinear time-varying systems. We establish the possibility of application of a perturbed parametrized system, by using Lyapunov theory, to the investigation of the robustness properties that may provide practical semiglobal uniform  exponential stability with respect to perturbations.