Stability and Controllability of Nonlinear Systems

Abstract

This paper is aimed at establishing new stability and controllability results for nonlinear systems. The approach is to use the Lyapunov indirect method to obtain the stability of the equilibrium solution of the uncontrolled nonlinear system by applying the Jacobi’s linearization method and the controllability of the controlled system obtained by the rank criterion for properness. Example is given with a real-life application to illustrate the effectiveness of the theoretical results.

Stability and controllability analysis of stochastic model for stock market prices

“…The stock price 𝑥(𝑡) of equation ( 3) can be expressed in the form of integral equation at time 𝑡 by using variation of constant formula (see) [21,24] to get…”

Stability and Feedback Control of Volterra Type Systems with Time Delay

“…Several methods of analysis are available in studying the stability of such systems which includes the Lyapunov-based [10], fixed point based [11] and spectral radius [12] approaches see [13] and other references therein for details). The Lyapunov based approach which is the focus of stability application in this research is widely used in studying stability theories as well as other qualitative and quantitative properties of linear and nonlinear delay differential systems see [14,15] and references therein. The Lyapunov based approach is classified into two major types; the Razumikhin approach [16,17] and the Krasovskii approach [18].…”