Incremental peak-to-peak gain computation and regulation of discrete-time positive Luré systems using linear programming

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 ℓ ∞ 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 ℓ ∞ incremental gain is verified by numerical examples.