Abstract
In this short chapter we will present one of the connections between operator theory and control theory. In Section 1 we will show how some of the previous H∞ optimization problems introduced in Chapter IX naturally arise in robust control theory. One of the simplest of these problems will be solved in Section 3, by another method inspired by the functional model theory presented in Section IX.5. For this purpose some useful operator theoretical preparations are given in Section 2.
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Notes And Comments
Francis, B.A., A Course in W° Control Theory, Lecture Notes in Control and Information Science, Springer, New York, 1987.
Doyle, J., Francis, B.A. and A. Tannenbaum, Classical Feedback Control Theory,Lecture notes (personal copy).
Helton, J.W., Operator Theory, Analytic Functions, Matrices, and Electrical Engineering, CBMS Regional Conference Series in Math., 68, Amer. Math. Soc., Providence, Rhode Island, 1987.
Bercovici, H., Operator Theory and Arithmetic in H°°, American Mathematical Society, Providence, Rhode Island, 1988.
Bercovici, H., Foias, C. and A. Tannenbaum, On skew Toeplitz operators I Topics in Operator Theory and Interpolation, Operator Theory: Advances and Applications,28 Ed. I. Gohberg (1988) pp. 21–43.
Foias, C., Tannenbaum, A. and G. Zames, On the W°-optimal sensitivity problem for systems with delays, SIAM J. Control and Optimization, 25 (1987) pp. 686–706.
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Foias, C., Frazho, A.E. (1990). Numerical Algorithms for H∞ Optimization in Control Theory. In: The Commutant Lifting Approach to Interpolation Problems. OT 44 Operator Theory: Advances and Applications, vol 44. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7712-1_12
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DOI: https://doi.org/10.1007/978-3-0348-7712-1_12
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-7714-5
Online ISBN: 978-3-0348-7712-1
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