Static Output Feedback Synthesis for MIMO LTI Constrained Positive Systems Using LP Approach

• 成果类型: Article
• 署名作者: Bolajraf, Mohamed
• 署名单位: Abdelmalek Essaadi University of Tetouan
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3514494
• 发表日期: 2025
• 页码: 3425-3432
• 关键词: Output feedback; Linear systems; vectors; Closed loop systems; Sufficient conditions; Iterative algorithms; asymptotic stability; State feedback; Autonomous systems; Adaptive control; Linear programming (LP); multiinput multioutput (MIMO) linear time-invariant (LTI) positive systems; stabilization with restricted sign control and nonsymmetrical constrained control; static output feedback controller

摘要

The aim of this article is to design static output feedback controllers for multi-input-multi-output (MIMO) linear time-invariant (LTI) systems, with the requirements of positivity and asymptotic stability to be guaranteed in closed-loop systems. By expressing the matrix product $KC$ as a sum of rank one matrices, new necessary and sufficient conditions for the existence of a static output feedback controller are derived in terms of linear programming (LP) conditions. One of the advantages of the proposed LP method is that constraints on the system can be dealt with explicitly and easily. Thus, by following this LP approach, other problems are solved, for instance, stabilization with restricted sign control, stabilization with nonsymmetrical constrained control, and stabilization with state constraint. Furthermore, this proposed technique is also used to derive an iterative LP algorithm, which computes the gain matrix of the static output feedback controller. Finally, illustrative examples confirm the effectiveness and applicability of theoretical results, and they also show that the proposed LP method has advantages over existing approaches.