Abstract
This deals with a generalized version of the standard matrix Riccati equations which arises in certain stochastic optimal control problems. A novelty here, regarding previous works, is that it is assumed that the systems are not necessarily detectable, including those having nonobservable modes on the imaginary axis. The collection of results which are derived in this paper includes, inter alia, the following: a) existence and uniqueness of nonnegative definite solutions of the generalized algebraic Riccati equations which give rise to stable closed loop systems in the case of non-detectable systems; b) new convergence results for the solution of the generalized Riccati differential equation under relatively weaker assumptions.
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© 1990 Birkhäuser Boston
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de Souza, C.E., Fragoso, M.D. (1990). Results on Generalised Riccati Equations Arising in Stochastic Control. In: Kaashoek, M.A., van Schuppen, J.H., Ran, A.C.M. (eds) Robust Control of Linear Systems and Nonlinear Control. Progress in Systems and Control Theory, vol 4. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4484-4_6
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DOI: https://doi.org/10.1007/978-1-4612-4484-4_6
Publisher Name: Birkhäuser Boston
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