Stability of Linear Time-Invariant Systems

It is well known that the stability of a linear time-invariant system can be determined using a Liapunov function of the quadratic form. However, for establishing the asymptotic stability of such a system for all linear negative feedback gains in a given range, a Liapunov function which yields both necessary and sufficient conditions has not been available so far. This correspondence presents such a function and affirms a recent conjecture of Narendra. The interest in this problem is due to its being a limiting case of the Lur'e problem