Capture zones of linear feedback pursuer strategies

The problem of intercepting maneuverable targets is considered using a linearized kinematical model with first-order acceleration dynamics of the interceptor and the target. Capture-guaranteeing strategies and the respective capture zones are constructed in a class of linear time-varying feedback pursuer strategies. Necessary and sufficient conditions for having a nontrivial capture zone are obtained. These conditions generalize the ones obtained previously. Explicit analytical description of the capture zone boundary is derived. In the numerical example, theoretical results are validated by the nonlinear simulation.