A constructive algorithm for stabilization of nonlinear neutral time-delayed systems occurring in bioengineering

Abstract

A criterion is given for the stabilization of the trivial solutions solution of a nonlinear functional differential equation of neutral type occurring in bioengineering under the assumptions of continuity and boundedness of the coefficients. The criterion is a condition on the roots of a certain ‘quasi-polynomial’, i.e. a polynomial in a variable and exponential of that variable. The derivation is based on a constructive algorithm which generates a stabilizing control. The method is illustrated by the construction of stabilizing control for a smooth per suit eye movement system. It is shown that for the synthesis of required control function it is unnecessary in a number of cases to solve the corresponding Riccati matrix equation; rather, it is sufficient to find the roots of a certain ‘quasi-polynomial’, i.e. a polynomial in a variable and exponential of that variable. The model of the smooth pursuit eye movement system can be mathematically described by a set of nonlinear, neutral, functional differential equations. This work deals with a novel way of designing a controller for stabilizing and tracking of a new model for the smooth pursuit system described by a nonlinear functional differential equations of neutral type. The eigenvalues of the system are shifted in a controlled manner using certain bilinear transformations. Simulation results are used to establish the validity of the results.