Abstract

In this paper, linear quadratic control is considered for linear time invariant (LTI) systems with dynamic output feedback. Firstly, a new matrix inequality is presented for LTI systems with quadratic criterion and Lyapunov function. Secondly, nonlinear matrix inequality is transformed into linear matrix inequalities (LMIs) with the ideas of elimination. Consequently, the synthesis of linear quadratic output feedback is transformed into solving LMIs optimization problem. Finally, a numerical example is included to illustrate the effectiveness of the proposed approach.

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