Abstract
In the last chapter, we considered the problem of minimizing F zw with respect to the H 2 norm. The performance specifications were given in the time domain. As we have seen in Chap. 3 for SISO problems, for specifications in the frequency domain the H ∞ norm is an adequate tool. In this way we are naturally lead to the question of how controllers can be characterized in a way which minimizes the closed-loop transfer function F zw with respect to the H ∞ norm. There are two important methods for solving this problem. One is based on two Riccati equations similar to those used in the H 2 problem. It will be analyzed in this chapter, whereas the other method uses linear matrix inequalities and is presented in the next chapter.
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Notes and References
Zames, G.: On the input-output stability of time-varying nonlinear feedback systems: Part I: Conditions derived using concepts of loop gain, conicity, and positiv-ity, IEEE Trans. Autom. Control, 11, pp. 228–238, 1966.
Doyle, J. C, Glover, K., Khargonakar, P. and Francis, B. A.: State-space solutions to standard H 2 and H ∞ control problems, IEEE Trans, on Autom. Control, 34, pp. 831–847,1989.
Glover, K., Limebeer, D. J. N., Doyle, J. C., Kasenally, E. .M. and Safanov, M. G.: A characterization of all solutions of the four block general distance problem, SIAM J. Control Optim., 29, pp. 283–324,1991.
Safonov, M. G., Limebeer, D. J. N., and Chiang, R. Y.: Simplifying the H ∞ theory via loop shifting, matriy pencil and descriptor concepts, Int. J. Control, 50, pp. 2467–2488,1990.
Zhou, K., Doyle, J. and Glover, K.: Robust and Optimal Control, Prentice Hall, Englewood Cliffs, New Yersey, 1995.
Sefton, J. and Glover, K.: Pole/zero cancellations in the general H ∞ problem with reference to a two-block design, Syst. Control Lett, 14, pp. 295–306, 1990.
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© 2004 Springer-Verlag Berlin Heidelberg
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Mackenroth, U. (2004). H∞ Optimal Control: Riccati-Approach. In: Robust Control Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-09775-5_9
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DOI: https://doi.org/10.1007/978-3-662-09775-5_9
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