The choice and use of normal approximations to transfer-function matrices of multivariable control systems
Ray W. Daniel, Basil Kouvaritakis · International Journal of Control · 1983
Approximating the transfer-function matrix of a multivariable system by a normal matrix provides a reliable way for assessing the stability of feedback systems in the presence of uncertainty or non-linearities. The appropriate stability results, however, must take into account the error in the approximation, and if this is large the stability assessment becomes conservative. The present paper proposes techniques for obtaining improved normal approximations and presents results which, for the 2 × 2 case, minimize the error of approximation. The approach is amenable to a numerically robust implementation on a digital computer and has obvious application in the analysis of feedback stability.