Robust control of uncertain multi-inventory systems via Linear Matrix Inequality

TL;DR

This paper develops LMI-based conditions for robust stabilization of uncertain multi-inventory systems with demand and control uncertainties modeled within ellipsoids or polytopes, aiming to reduce inventory costs.

Contribution

It introduces novel LMI conditions for stabilizing multi-inventory systems with uncertainties using saturated linear feedback controls, advancing robust control methods.

Findings

LMI-based stabilizability conditions derived for uncertain inventory systems

Effective control strategies for reducing inventory costs under uncertainties

Application of recent polytopic system analysis techniques

Abstract

We consider a continuous time linear multi inventory system with unknown demands bounded within ellipsoids and controls bounded within ellipsoids or polytopes. We address the problem of "-stabilizing the inventory since this implies some reduction of the inventory costs. The main results are certain conditions under which "-stabilizability is possible through a saturated linear state feedback control. All the results are based on a Linear Matrix Inequalities (LMIs) approach and on some recent techniques for the modeling and analysis of polytopic systems with saturations.