Maximal and Stabilizing Hermitian Solutions for Discrete-Time Coupled Algebraic Riccati Equations |
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Authors: | O L V Costa R P Marques |
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Affiliation: | Department of Electronic Engineering, University of S?o Paulo, Av. Prof. Luciano Gualberto—travessa 3, 158, 05508-900 S?o Paulo SP, Brazil. {oswaldo, rpm}@lac.usp.br., BR
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Abstract: | Discrete-time coupled algebraic Riccati equations that arise in quadratic optimal control and H
∞-control of Markovian jump linear systems are considered. First, the equations that arise from the quadratic optimal control
problem are studied. The matrix cost is only assumed to be hermitian. Conditions for the existence of the maximal hermitian
solution are derived in terms of the concept of mean square stabilizability and a convex set not being empty. A connection
with convex optimization is established, leading to a numerical algorithm. A necessary and sufficient condition for the existence
of a stabilizing solution (in the mean square sense) is derived. Sufficient conditions in terms of the usual observability
and detectability tests for linear systems are also obtained. Finally, the coupled algebraic Riccati equations that arise
from the H
∞-control of discrete-time Markovian jump linear systems are analyzed. An algorithm for deriving a stabilizing solution, if
it exists, is obtained. These results generalize and unify several previous ones presented in the literature of discrete-time
coupled Riccati equations of Markovian jump linear systems.
Date received: November 14, 1996. Date revised: January 12, 1999. |
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Keywords: | , Maximal hermitian solutions, Stabilizing solutions, Coupled algebraic Riccati equations, Quadratic optimal control,,,,,,H∞,-Control, |
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