2009•IEEE Transactions on Automatic ControlRequires access

Solving the Matrix Differential Riccati Equation: A Lyapunov Equation Approach

Zoran Gajić

Abstract

In this technical note, we investigate a solution of the matrix differential Riccati equation that plays an important role in the linear quadratic optimal control problem. Unlike many methods in the literature, the approach that we propose employs the negative definite anti-stabilizing solution of the matrix algebraic Riccati equation and the solution of the matrix differential Lyapunov equation. An illustrative numerical example is provided to show the efficiency of our approach.

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Key concepts: Algebraic Riccati equation, Riccati equation, Linear-quadratic regulator, Mathematics, Lyapunov equation, Matrix differential equation, Differential equation, Matrix difference equation