Title:   Structured condition numbers for symmetric algebraic Riccati equations

Algebraic Riccati equations arise in optimal control problems in continuous and discrete time. With multiple state variables and multiple control variables, the Riccati equations are linear-quadratic matrix equations. Perturbation analysis reveals the sensitivity of the solution to the input data. Condition number is a measurement of the sensitivity, that can be used to estimate the error in the computed solution. Assuming the structure of the perturbation is the same as that of the data, we present a structured perturbation analysis of the continuous and discrete symmetric algebraic Riccati equations. We define and derive structured normwise, mixed, and componentwise condition numbers for symmetric algebraic Riccati matrix equations using the Kronecker product. Also, we give an efficient and practical condition number estimation method by applying the small sample condition estimation method.