Stability analysis and control of non-standard nonlinear singularly perturbed system

Abstract

Stability analysis and control of a non-standard nonlinear singularly perturbed system are studied. A non-standard form in which linear and nonlinear parts coexist is considered and a transformation using linear parts is suggested. On the basis of this transformation, the non-standard form is changed into a quasi-standard form, which is similar to a standard form. For the transformed system, the stability conditions under which the system is exponentially stable for the sufficiently small perturbation parameter epsilon are found. Using this analysis, a stabilising controller is designed. The practical aspects of the scheme proposed are illustrated through the control of a series DC motor.