Incremental Gain Computation and Regulation of Discrete-time Positive Luré Systems using Linear Programming

This work approaches the problem of computing incremental ${\mathrm{\ell }}_1$ and ${\mathrm{\ell }}_{\mathrm{\infty }}$ gains for discrete-time positive systems in \lure feedback with static memoryless nonlinearities, and regulating the ${\mathrm{\ell }}_{\mathrm{\infty }}$ gain through the design of a state-feedback controller. Finite incremental gains provide a quantitative measure of robustness for trajectories, and will ensure that all pairs of trajectories will converge to a fixed point or will diverge together in the absence of an applied input. Upper-bounds on these incremental gains can be computed through linear programming. Computation and regulation of the ${\mathrm{\ell }}_1$ and ${\mathrm{\ell }}_{\mathrm{\infty }}$ incremental gains are verified by numerical examples.