Computation of peak output for inputs satisfying many bounding conditions on magnitude and slope

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

“…The second addend depends on b(t) in Eq. (18) and captures the effect of applying an arbitrary number of input signals.…”

“…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.…”

Design of nonlinear feedback systems with inputs and outputs satisfying bounding conditions

“…In addition, P has been employed in practical applications (see, for example, [11], [12]) and been investigated in, for example, [1], [2], [5], [13], [6]. It may be noted further that when all the possible inputs do not have stepwise discontinuities, using P as the possible set makes the design formulation more realistic and more appropriate than using L ∞ .…”

“…It should be noted that criterion (1) is frequently used in practice to monitor the performances of the control systems and has long been investigated by many authors (see, for example, [1], [2], [3], [4], [5], [6] and also the references therein). Moreover, the condition becomes remarkably useful in the design of critical systems [7], [4] (see also [8]), where any violation of the bound ε may give rise to unacceptable consequences.…”

“…So far, the problem of computingê andû, and hence that of solving the design criteria (4), have been investigated only for cases of linear time-invariant systems (see, for example, [1], [14], [12], [6] and also the references therein). In general, computing the peaksê andû for general nonlinear systems are extremely difficult, since the optimization problems defined in (4) are non-convex and infinite-dimensional.…”