An Assessment of the Effect of Varying Popov’s Parameter on the Region of Robust Absolute Stability of Nonlinear Impulsive Control Systems with Parametric Uncertainty

Abstract

This paper focuses on finding and the assessment of the variation of the region of robust absolute stability of an impulse control system, with monotonous nonlinearities, as Popov’s parameter varies. A mathematical model of a nonlinear impulsive control system (NICS) is considered. The criterion for absolute stability on the equilibrium position for NICS, with monotonous nonlinearities, can be expressed as a polynomial expression. The robust stability of NICS is tested using Kharitonov’s theorem and a modified root locus method for interval transfer functions. A graphical illustration of roots of the characteristic equation, which have been gotten from the interval transfer function, on the complex plane is used in the assessment of the stability of control system. To evaluate the effect of Popov’s parameter, a specially written program complex Stability is used. An illustrative example is given to demonstrate the effect of varying Popov’s parameter on the region of absolute robust stability.