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A computational method for simultaneous LQ optimal control design via piecewise constant output feedback

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2 Author(s)
Yong-Yan Cho ; Dept. of Electr. & Comput. Eng., Virginia Univ., Charlottesville, VA, USA ; Lam, J.

The paper is concerned with simultaneous linear-quadratic (LQ) optimal control design for a set of LTI systems via piecewise constant output feedback. First, the discrete-time simultaneous LQ optimal control design problem is reduced to solving a set of coupled matrix inequalities and an iterative LMI algorithm is presented to compute the feedback gain. Then, simultaneous stabilization and simultaneous LQ optimal control design of a set of LTI continuous-time systems are considered via periodic piecewise constant feedback gain. It is shown that the design of a periodic piecewise constant feedback gain simultaneously minimizing a set of given continuous-time performance indexes can be reduced to that of a constant feedback gain minimizing a set of equivalent discrete-time performance indexes. Explicit formulas for computing the equivalent discrete-time systems and performance indexes are derived. Examples are used to demonstrate the effectiveness of the proposed method

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Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on  (Volume:31 ,  Issue: 5 )