An application of two dimensional stability criterion to a special class of distributed parameter systems

The conditions of stability independent of time delay and distributed lag of a special class of distributed parameter systems are obtained in terms of a two dimensional stability criterion. As the first step, a two-variable polynomial is generated from the characteristic function of such a system, and then a two dimensional stability test is applied. The results show whether the given system is stable independently of the time delay, and whether it is stable independently of distributed lag, depending on the form of the characteristic function of the system. Illustrative examples are included