<p>This study investigates a switching system comprising two unstable focus subsystems, two unstable node subsystems, and two saddle point subsystems. The primary objective is to design an optimal state-dependent switching rule, so that the solution trajectories of the switching system can converge to the origin at the maximum possible rate. To intuitively characterize the convergence behavior of the solution trajectories under different switching modes, a polar coordinate transformation is first applied to represent the subsystems. Subsequently, an integral index is constructed to quantify the changes in the polar radius for the switching system under spinning and chattering switching strategies, respectively. In order to choose the most suitable switching mode and determine the optimal positioning of the switching lines, a comprehensive regional division and phase plane analysis is conducted. This analysis fully considers key structural features, including the relative positions of subsystem-specific boundary lines and the rotation directions of the solution trajectories. For switching systems with unstable focus and unstable node subsystems, the optimal state-dependent switching rules are derived by minimizing the constructed integral indices. In the case of two saddle point subsystems, the stabilizing factors of both subsystems are leveraged to design a state-dependent switching rule that minimizes the integral index as much as possible. Finally, four comparative simulations in comparison with existing studies validate that the resulting switching rules can significantly enhance the convergence speed of the system states.</p>