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Extended {\rm H}_{2} Controller Synthesis for Continuous Descriptor Systems

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3 Author(s)
Yu Feng ; IRCCyN (Inst. de Rech. en Commun. et Cybernetique de Nantes), Nantes, France ; Mohamed Yagoubi ; Philippe Chevrel

This technical note presents a complete solution to the nonstandard H2 output feedback control problem for continuous descriptor systems where unstable and nonproper weighting functions are used. In such a problem, the desired controller has to satisfy two conditions simultaneously: (i) the closed-loop is admissible and has a minimum H2 norm, (ii) only the internal stability of a part of the closed-loop is sought. The condition of the existence of such a controller is deduced. An explicit characterization of the optimal solution is also formulated, based on two generalized algebraic Riccati equations (GAREs) and two generalized Sylvester equations. A numerical example is included to illustrate the validity of the proposed results.

Published in:

IEEE Transactions on Automatic Control  (Volume:57 ,  Issue: 6 )