On the $\tau $-Decomposition Method of Stability Analysis for Retarded Dynamical Systems

This paper deals with a method of studying the effects of the amount of time delay on the stability of dynamical. systems. The method of analysis involves first decomposing the positive time delay axis into many intervals within each of which the stability character remains unchanged. For the change of stability character from interval to interval the result is expressed geometrically in terms of leaving or entering of a unit circle by a curve which is determined by a rational function. The paper extends the work of Krall and extends and modifies the earlier work of Sokolov and Miasnikov.