Incremental Peak-to-Peak Gain Computation and Regulation of Discrete-Time Positive Luré Systems using Linear Programming

Jared Miller

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arXiv · 2505.24386

Incremental Peak-to-Peak Gain Computation and Regulation of Discrete-Time Positive Luré Systems using Linear Programming

Jared Miller

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Abstract

Incremental gains provide a quantitative measure of robustness for trajectories of a dynamical system. Finite incremental gains ensure that all pairs of trajectories will together converge to a fixed point or will diverge together in the absence of an applied input. This work approaches the problem of computing the incremental peak-to-peak gains for positive linear systems in Luré feedback with static memoryless nonlinearities, and regulating the incremental $\ell_\infty$ gain through the design of a state-feedback controller. Upper-bounds on these incremental gains can be computed through linear programming. Computation and state-feedback regulation of the $\ell_\infty$ incremental gain is verified by numerical examples.

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Jared Miller. 2026-09-05. Incremental Peak-to-Peak Gain Computation and Regulation of Discrete-Time Positive Luré Systems using Linear Programming. https://arxiv.org/abs/2505.24386

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