A note on stability calculations and time lag
The question is: what are the conditions on a, b, /3, and c which are necessary and sufficient that the real parts of all the roots be negative, thus indicating stability. There also have appeared papers in pure mathematics2 which discuss similar problems and which supply useful techniques for their solutions. It is the purpose of this note to indicate how one such technique, which shall be referred to as the Cauchy-Sturm method, may be applied to a discussion of the zeros of transcendental expressions such as (1). Equation (1) arises in the study of control systems with retarded action or time lags.3 Several attempts have been made to study the zeros of this function and the results have not been consistent. Minorsky,4 in one of his papers, expands the function in a power series