Abstract
In this contribution we want to draw the readers’s attention to an open problem that concerns the existence of certain solutions to the algebraic Riccati equation. Since its introduction in control theory by Kalman in the beginning of the sixties, the algebraic Riccati equation has known an impressive range of applications, such as linear quadratic optimal control, stability theory, stochastic filtering and stochastic control, stochastic realization theory, the synthesis of linear passive networks, differential games, and H ∞ optimal control and robust stabilization. For an overview of the existing literature on the algebraic Riccati equation, we refer to [3].
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Trentelman, H.L. (1999). When does the algebraic Riccati equation have a negative semi-definite solution?. In: Blondel, V., Sontag, E.D., Vidyasagar, M., Willems, J.C. (eds) Open Problems in Mathematical Systems and Control Theory. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-0807-8_44
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DOI: https://doi.org/10.1007/978-1-4471-0807-8_44
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