Improving output bound computation for continuous-time LTI systems

This paper presents a set invariance method to compute an output bound for a continuous-time linear time-invariant (LTI) system given sets of initial conditions and external disturbances. The proposed method aims to reduce conservatism compared to existing methods by incorporating the transient time information and the Lyapunov function’s decay rate. Two new methods are introduced to obtain the transient time information by numerically computing an upper bound of the output derivative through matrix inequalities. Interestingly, overshoot analysis is a special case for which our approach can significantly improve the overshoot bound. The effectiveness of our method is showcased in an illustrative example of a PID-controlled-mass system.