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On the Sensitivity of Algebraic Riccati Equations

By Ji-guang Sun


Consider the continuous-time algebraic Riccati equation (CARE) and the discrete-time algebraic Riccati equation (DARE) which arise in linear control and system theory. Appropriate assumptions on the coe#cient matrices guarantee the existence and uniqueness of symmetric positive semidefinite stabilizing solutions. In this paper, we apply the theory of condition developed by Rice to define condition numbers of the CARE and DARE in the Frobenius norm, and derive explicit expressions of the condition numbers in a uniform manner.

Year: 2007
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