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    This study enhances parameter space methods for control system design, enabling zero or constrained elements in feedback gain matrices. The improved technique efficiently handles complex structural constraints and avoids oscillatory dynamics.

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    Area of Science:

    • Control Theory
    • Systems Engineering
    • Optimization

    Background:

    • Optimal control and system design often require feedback gain matrices with specific structural constraints.
    • Existing parameter space methods offer solutions but face limitations in constraint types, stability, and computational efficiency.

    Purpose of the Study:

    • To extend parameter space methods for a broader class of structural constraints in feedback gain matrices, including zero elements and intrarow/intracolumn constraints.
    • To enhance computational efficiency and ensure stable closed-loop dynamics.

    Main Methods:

    • A procedure to transform the original system into an extended system with a decentralized feedback matrix.
    • Mapping rules to the parameter space for decentralized feedback matrices with intrarow and intracolumn constraints.
    • Inclusion of closed-loop dominant pole constraints and a revised cutting plane logic for improved optimization efficiency.

    Main Results:

    • The proposed method effectively handles structural constraints, including zero elements and intrarow/intracolumn limitations in the gain matrix.
    • The approach ensures avoidance of oscillatory closed-loop dynamics through dominant pole constraints.
    • Computational efficiency is improved by allowing multiple linear constraints per iteration.

    Conclusions:

    • The enhanced parameter space method successfully addresses limitations of previous approaches for structured control problems.
    • The technique is effective for designing feedback gain matrices with complex structural requirements.
    • Simulation examples validate the proposed method's effectiveness and efficiency.