Asymptotic behavior of root-loci in multivariable systems

Abstract

Asymptotic behavior of the root-loci of Linear, time-invariant, multivariable, and negative unity feedback system is studied in relation to the system stability and its performance. As the feedback gain goes to infinity, some of the loci terminate to certain finite points, which are called Finite Zeros, while the others terminate to certain imaginary points at infinity along the asympotes, which are called Infinite Zeros. Kouvaritakis and Edmunds presented algorithms to find the finite and infinite zeros, and then to design controllers to improve the stability of a given system. In this work, since the design algorithm formulated by them is proven to be not valid in general, a new design algorithm is suggested. The computer programs and numerical schemes are developed to compute the finite and infinite zeros, and then to be used in designing a controller for better stability.