Linear Programming Approach to Constrained Stabilization of Positive Differential‐Difference Equations With Unbounded Delay

• Published in: Optimal control applications & methods
• Main Authors: Sau, N. H., Niamsup, P., Phat, V. N.
• Format: Journal Article
• Language: English
• Published: 15.08.2025
• ISSN: 0143-2087; 1099-1514
• DOI: 10.1002/oca.70015

This article addresses the constrained stabilization problem for a class of linear positive differential‐difference equations (DDEs) characterized by unbounded time‐varying delays and subject to bounded control constraints. We propose an efficient methodology rooted in linear programming (LP) to design stabilizing state feedback controllers. The core contributions include the development of novel characterizations for system positivity and the comparison principle tailored to this specific class of DDEs. Based on these characterizations, we establish sufficient conditions for the existence of admissible state feedback controllers that guarantee both positivity and asymptotic stability of the closed‐loop system while respecting the control input constraints. Crucially, these conditions are formulated as a set of linear inequalities, rendering the controller design problem solvable via standard LP techniques. The effectiveness and practical applicability of the theoretical results are demonstrated through comprehensive numerical examples.