Abstract
This review is concerned with two algebraic Riccati equations. The first is a quadratic matrix equation for an unknown n × n matrix X of the form
where A, D, C are n × n complex matrices with C and D hermitian. Further hypotheses are imposed as required, although Section 2.3 contains some discussion of more general non-symmetric quadratic equations. The second equation has the fractional form
where R and Q are hermitian m × m and n × n matrices, respectively, and A, B, C are complex matrices with respective sizes n × n, n × m, and m × n. The two equations are frequently referred to as the “continuous” and “discrete” Riccati equations, respectively, because they arise in physical optimal control problems in which the time is treated as a continuous variable, or a discrete variable.
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Lancaster, P., Rodman, L. (1991). Solutions of the Continuous and Discrete Time Algebraic Riccati Equations: A Review. In: Bittanti, S., Laub, A.J., Willems, J.C. (eds) The Riccati Equation. Communications and Control Engineering Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58223-3_2
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DOI: https://doi.org/10.1007/978-3-642-58223-3_2
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