H∞ control via dynamic output feedback for positive systems with multiple delays


This study is worried with H∞ management issues for positive systems with time delays using dynamic output feedback. Novel bounded real lemma for continuous-time systems with time delays is initial presented, that shows one of the outstanding properties of diagonal positive definite matrix solutions to linear matrix inequalities for positive systems. The proposed results reveal that H∞ norms of positive systems with time delays in state and output equations are corresponding to that of the corresponding systems with zero delays. The positivity preserving H∞ control problem by means that of dynamic output feedback is additionally considered, and therefore necessary and sufficient conditions in the kinds of matrix equalities are established for the solvability of such problem. The desired controller gains can be obtained by suggests that of cone complementarity linearisation techniques. A numerical example is finally given to illustrate the effectiveness of the obtained results.

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