Finite-time stability analysis of proportional navigation guidance system

The finite time stability of proportional navigation guidance system is presented. A linearized proportional navigation guidance loop is introduced. The reassembled model of guidance loop exhibits a famous Lur´e system which consisting of a linear time-invariant element and a time-varying part. It is shown that a sufficient condition for stability, with 1≤p≤∞, is obtained by utilizing the well-known small gain theorem. Based on the condition of system stability, the relation between guidance loop stability and miss distance is proved. It is proved that, if the linear time-invariant part of the system belongs to the class of positive real transfer functions, the guidance system is stable and the guidance system can achieve zero miss distance.