On computing the worst-case norm of linear systems subject to inputs with magnitude bound and rate limit

The closed-form solution for the worst-case norm of linear systems subject to inputs with magnitude bound and rate limit

“…The reader is referred to [2], for the detailed comparison between the WCN obtained via different numerical methods and the exact WCN computed using the closed-form solutions proposed in this paper. VI.…”

“…While the derivative is zero, the input magnitude is ±M [1], [2], [4]- [6]. In other words, at any time instant, w(t) is equal to magnitude limit or its derivative is equal to rate limit.…”

“…In [1], Lane has given a summation of integral that represents the WCN when the step response under consideration is 1 − e −t sin(ωt + π/2), for some ω, which however cannot be realized by any LTI system. In this paper, the characteristics of the worstcase input follow the previous development [1], [2], [4]- [6]. Then, we derive the worst-case inputs and obtain closed-form expressions of the WCN for second-order LTI systems.…”

“…To evaluate the accuracy of numerical methods for computing the WCN [1], [2], we have to test on some benchmark problems or determine analytical WCN solutions of certain LTI systems. In this work, we focus on deriving the WCN for a class of second-order LTI systems.…”

Outputs bounds for linear systems with repeated input signals: existence, computation and application to vehicle platooning

“…Different operator norms are defined in [14,15], while [16] provides explicit formulas for their evaluation. Several conditions of the L 2 and L ∞ norm of the input signal and its slope are used in [17,18]. Different from the setting in this paper, the cited approaches do not address the application of repeated input signals and do not consider time-limited input signals.…”