Exponential stability and L۲ gain analysis for systems with infinite distributed delay by scalar kernels to track a surface vessel by submarine

In this paper, the problem of trajectory optimization in tracking the location of surface moving targets by measuring the side angle alone is studied. The performance of target tracking with side angle alone depends on the stability of the target position in the target observer's motion path or the optimal observer maneuver. First, the modeling of the path control problem is performed by the kernel-scalar matrix method. Then, by analyzing the L۲interest rate, the control law is obtained for moving independently of the initial conditions. The advantages of the proposed modeling are maximizing the delay limit for the stability of the entire maneuver time, calculating the control rule at the start of the maneuver and high flexibility in applying the travel restrictions. The efficiency of the method presented by simulation with scalar kernel matrix method with control methods of delayed systems with distributed delay is shown and compared by recent references. Performance is also evaluated in different scenarios and its reliability is checked. This method is also used in the practical problem of tracking a surface vessel by submarine.