This paper presents the solution of the linear optimal control problem using derivative feedback for continuous, time-invariant, linear systems. The state-derivative and output-derivative feedback controllers are investigated. In this work, the optimal feedback gain matrices are derived which minimize the non-standard quadratic performance index. An explicit expression of the optimal state-derivative feedback gain is derived. Additionally, a convergent algorithm to solve the output-derivative feedback gains is demonstrated. The problems are studied for non-singular and singular open-loop state matrices. The necessary conditions for the existence of optimal gains are established. Finally, simulation results are included to show the effectiveness of the proposed approach.
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