A new characterization of invariant subspaces of H2 and applications to the optimal sensitivity problem

This paper gives a new equivalent characterization for invariant subspaces of H 2 , when the underlying structure is specified by the so-called pseudorational transfer functions. This plays a fundamental role in computing the optimal sensitivity for a certain important class of infinite-dimensional systems, including delay systems. A closed formula, easier to compute than the well-known Zhou–Khargonekar formula, is given for optimal sensitivity for such systems. An example is given to illustrate the result. © 2004 Elsevier B.V. All rights reserved.

[1]  Bassam Bamieh,et al.  A general framework for linear periodic systems with applications to H/sup infinity / sampled-data control , 1992 .

[2]  S. Hara,et al.  Worst-case analysis and design of sampled-data control systems , 1993, IEEE Trans. Autom. Control..

[3]  W. Donoghue.  Distributions and Fourier transforms , 1969 .

[4]  Kentaro Hirata,et al.  A Hamiltonian-based solution to the two-block H∞ problem for general plants in H∞ and rational weights , 2000 .

[5]  Shinji Hara,et al.  Relationships between internal and external stability for infinite-dimensional systems with applications to a servo problem , 1987 .

[6]  L. Schwartz.  Théorie des distributions , 1966 .

[7]  Yutaka Yamamoto,et al.  Pseudo-rational input/output maps and their realizations: a fractional representation approach to in , 1988 .

[8]  Malcolm C. Smith.  Singular values and vectors of a class of Hankel operators , 1989 .

[9]  Pramod Khargonekar,et al.  Weighted sensitivity minimization for delay systems , 1986, 1986 25th IEEE Conference on Decision and Control.

[10]  Hitay Özbay,et al.  Robust Control of Infinite Dimensional Systems: Frequency Domain Methods , 1996 .

[11]  Yutaka Yamamoto,et al.  Some remarks on Hamiltonians and the infinite-dimensional one block H ∞ problem , 1996 .

[12]  P. Khargonekar,et al.  On the weighted sensitivity minimization problem for delay systems , 1987 .

[13]  Bassam Bamieh,et al.  A General Framework for Linear Periodic Sampled-Data Control Systems with Applications to , 1992 .

[14]  Allen Tannenbaum,et al.  Weighted sensitivity minimization: General plants in H ∞ and rational weights , 1987 .

[15]  Yutaka Yamamoto,et al.  Reachability of a class of infinite-dimensional linear systems: an external approach with applicatio , 1989 .

[16]  K. Hoffman.  Banach Spaces of Analytic Functions , 1962 .

[17]  On the mixed sensitivity optimization problem for stable pseudorational plants , 2003 .

[18]  Yutaka Yamamoto,et al.  Equivalence of internal and external stability for a class of distributed systems , 1991, Math. Control. Signals Syst..

[19]  W. Rudin.  Real and complex analysis , 1968 .