Stability of nonlinear m-perturbed feedback controls systems

Abstract

This paper examines the global and local stability of unstable nonlinear first- and second-order dynamical systems and the necessary conditions. More precisely, global and local stability is attained when these systems are controlled by m-perturbed feedback input controls functions. Finally, we obtain a dynamical system with m-perturbed feedback controls, a summation form with a nonlinear function that is exploited, and the stability of the systems supported by some illustrative examples.