This article describe about Algebraic Riccati Equation, which is not restrictive for Riccati equations arising in control of infinitedimensional systems. It is a type of nonlinear equation that arises in the context of infinitehorizon optimal control problems in continuous time or discrete time. It is verified by the time invariant solutions of the matrix valued Riccati difference equation, which is the analogue of the Riccati differential equation in the context of discrete time LQR. Algebraic Riccati Equation determines the solution of the infinitehorizon timeinvariant LinearQuadratic Regulator problem (LQR) as well as that of the infinite horizon timeinvariant LinearQuadraticGaussian control problem (LQG).
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