Stability and Controllability of Nonlinear Systems
S. T. Cotterell
Department of Mathematics, Rivers State University, P.M.B. 5080, Port Harcourt, Rivers State, Nigeria.
I. Davies *
Department of Mathematics, Rivers State University, P.M.B. 5080, Port Harcourt, Rivers State, Nigeria.
L. C. Abraham
Department of Mathematics, Rivers State University, P.M.B. 5080, Port Harcourt, Rivers State, Nigeria.
*Author to whom correspondence should be addressed.
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.
Keywords: Stability, Lyapunov indirect method, controllability, mass-spring-damper, non-linear system.