<p>Unlike conventional single-mode systems, switched linear systems are often suffered from excessive overshoot and prolonged settling time. This paper proposes a constructive methodology to optimize the transient performance of such systems. First, theoretical estimates for both the overshoot and settling time are derived. By employing the S-Lemma, the obtained upper bound for overshoot is proved to be tight. Second, an Interactive Transient Performance Optimization Algorithm is introduced to simultaneously optimize both overshoot and settling time. Under the condition that the system is stabilizable, the algorithm is guaranteed to converge within a finite number of steps. Third, a Minimum Settling Time Path Generation Algorithm with lower time complexity is proposed to exclusively optimize the settling time. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed algorithms.</p>