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

2025/05/30 by Miller, Jared
#FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2505.24386

Abstract

This work approaches the problem of computing incremental ℓ₁ and ℓ_∞ gains for discrete-time positive systems in \lure feedback with static memoryless nonlinearities, and regulating the ℓ_∞ 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 ℓ₁ and ℓ_∞ incremental gains are verified by numerical examples.

Citations

• Mitigating Transient Bullwhip Effects Under Imperfect Demand Forecasts
• A linear dissipativity approach to incremental input-to-state stability for a class of positive Lur'e systems
• Data-driven representations of conical, convex, and affine behaviors
• Optimization Algorithm Synthesis based on Integral Quadratic Constraints: A Tutorial
• L₂₊ Induced Norm Analysis of Continuous-Time LTI Systems Using Positive Filters and Copositive Programming
• On Contraction Analysis for Non-linear Systems
• Polyhedral Estimation of L-1 and L-infinity Incremental Gains of Nonlinear Systems

Related

• A linear dissipativity approach to incremental input-to-state stability for a class of positive Lur'e systems
• Robust Stability Analysis of Positive Lure System with Neural Network Feedback
• Controller for Incremental Input-to-State Practical Stabilization of Partially Unknown systems with Invariance Guarantees
• Polyhedral Estimation of L-1 and L-infinity Incremental Gains of Nonlinear Systems
• Stability Analysis of Discrete-time Lure Systems with Slope-restricted Odd Monotonic Nonlinearities