Analysis of guidance laws with non-monotonic line-of-sight rate convergence

This study presents analyses of guidance laws that involve non-monotonic convergence in heading error from a new perspective based on an advanced stability concept. Pure proportional navigation with range-varying navigation gain is considered, and the gain condition to guarantee asymptotic convergence to the collision course is investigated while allowing the heading error to exhibit patterns that involve intermediate diversion. The extended stability criterion considered in this study allows local increase of the function in some finite intervals, which is less conservative than the standard stability theorem. The existing guidance laws involving intentional modulation of the heading error as well as the design of the navigation gain are discussed with respect to the new stability criterion.