Distributed L₂-gain control of large-scale systems: A space construction approach

Area of Science:

• Control Theory
• Systems Engineering
• Applied Mathematics

Background:

• Distributed control of large-scale systems presents challenges due to high dimensionality.
• Classical control methods are often unsuitable for transformed high-dimensional systems.
• The L2-gain control problem requires ensuring stability and bounded energy gain.

Purpose of the Study:

• To develop a novel approach for the distributed L2-gain control problem in discrete-time large-scale systems.
• To establish necessary and sufficient conditions for stability and prescribed L2-gain.
• To design distributed controllers for these complex systems.

Main Methods:

• Transformation of the large-scale system into an equivalent high-dimensional representation.
• Application of a space construction approach to derive stability conditions.
• Formulation of conditions using linear matrix inequalities (LMIs).
• Development of a matrix construction method for controller design based on LMI solutions.

Main Results:

• Necessary and sufficient conditions for asymptotic stability and prescribed L2-gain are derived using LMIs.
• A method for constructing distributed controllers is presented, guaranteeing closed-loop stability and the desired L2-gain.
• The effectiveness of the proposed theoretical results is validated through two illustrative examples.

Conclusions:

• The proposed LMI-based approach effectively addresses the distributed L2-gain control problem for discrete-time large-scale systems.
• The developed method provides a systematic way to design distributed controllers with guaranteed stability and performance.
• The findings offer a valuable contribution to the field of robust control for complex networked systems.