Short-time stability of proportional navigation guidance loop

Stability characteristics of proportional navigation (PN) guidance are analyzed by using the short-time stability criterion which is extended here to accommodate time-varying state weights and time-varying bounds of the state norm. As short-time stability is defined over a specified time interval, its application to the stability analysis of a homing guidance loop that operates up to a finite time gives more accurate results than previous studies. Furthermore, within the framework of short-time stability, zero effort miss and acceleration command, which are the most important variables determining guidance performance, can be directly related with guidance loop stability. An application to a PN guidance loop with a 1st-order missile/autopilot time lag shows that the stability condition based on short-time stability is less conservative than the previous results based on hyperstability and Popov stability.