Finite Time Stability Approach to Proportional Navigation Systems Analysis

The e nite time stability of proportional navigation guidance systems is considered. Assuming planar geometry and linear missile dynamics, a proportional navigation missile ‐target guidance model is e rst formulated. The model exhibitsa feedback cone guration consisting of a lineartime-invariant element and a time-varying gain. The dee nition of e nite timeglobal absolutestability isthen presented. Itisshown that by employing thecirclecriterion, the e nite time stability of the guidance dynamics can be analyzed. An analytic bound for the time of e ight up to which stability can be assured is established. The bound depends on the system parameters and the time of e ight. Less conservative results, as compared to previous works, are obtained. This approach enables not only analysis of the system behavior for given missile dynamics, but more importantly, enables generation of a tool for system design. Illustrative examples are presented showing the effect of the system parameters on the bound. In addition, some design implications, such as the relation to miss distance, are outlined.