Jonathan R. Partington

Worst-case control-relevant identification

Abstract This paper introduces the reader to several recent developments in worst-case identification motivated by various issues of modelling of systems from data for the purpose of robust control design. Many aspects of identification in H ∞ and l 1 are covered including algorithms, convergence and divergence results, worst-case estimation of uncertainty models, model validation and control relevancy issues.

Brief Analysis of fractional delay systems of retarded and neutral type

This paper analyses several properties linked to the robust control of fractional differential systems with delays. The BIBO stability of both retarded and neutral fractional delay systems is related to the location of their poles. In the particular case of retarded systems, we give some properties of the poles of the system and the singular values of its Hankel operator.

Robust identification and interpolation in H

Abstract We consider system identification in H∞ in the framework proposed by Helmicki, Jacobson and Nett. An algorithm using the Jackson polynomials is proposed that achieves an exponential convergence rate for exponentially stable systems. It is shown that this, and similar identification algorithms, can be successfully combined with a model reduction procedure to produce low-order models. Connections with the Nevanlinna-Pick interpolation problem are explored, and an algorithm is given in which the identified model interpolates the given noisy data. Some numerical results are provided for illustration. Finally, the case of unbounded random noise is discussed and it is shown that one can still obtain convergence with probability 1 under natural assumptions.

Robust identification in H

Abstract We consider system identification in the Banach space H ∞ in the framework proposed by Helmicki, Jacobson, and Nett. It is shown that there is no robustly convergent linear algorithm for identifying exponentially stable systems in the presence of noise which is not tuned to prior information about the unknown system or noise. Various nonlinear algorithms, some closely related to one of Gu and Khargonekar, are analysed, and results on trigonometric interpolation used to provide new error bounds. An application of these techniques to approximation is given, and finally some numerical results are provided for illustration.

Coprime factorizations and stability of fractional differential systems

We give a frequency-domain approach to stabilization for a large class of systems with transfer functions involving fractional powers of s. A necessary and sufficient criterion for BIBO stability is given, and it is shown how to construct coprime factorizations and associated Bezout factors in order to parametrize all stabilizing controllers of these systems.

Rational approximation of a class of infinite-dimensional systems I: Singular values of hankel operators

In order to establish the optimal rates of convergence for the infinity-norm rational approximation problem, upper and lower bounds on the singular values of a class of Hankel operators are established. These asymptotically accurate estimates are derived from results on the singular values of Hankel operators with symbol equal to the product of a rational function and an exponential function, combined with results on Hankel integral operators (in continuous time) whose kernels have certain smoothness properties.

Robust identification of strongly stabilizable systems

For strongly stabilizable systems for which a strongly stabilizing controller is known approximately, the authors consider system identification in the graph, gap, and chordal metrics using robust H/sub infinity / identification of the closed-loop transfer function in the framework proposed by A.J. Helmicki et al. (1990). Error bounds are derived showing that robust convergence is guaranteed and that the identification can be satisfactorily combined with a model reduction step. Two notions of robust identification of stable systems are compared, and an alternative robust identification technique based on smoothing, which can be used to yield polynomial models directly, is developed. >

H∞ and BIBO stabilization of delay systems of neutral type

Frequency-domain tests for the H∞ and BIBO stability of large classes of delay systems of neutral type are derived. The results are applied to discuss the stabilizability of such systems by finite-dimensional controllers.

Robust stabilization of delay systems by approximation of coprime factors

Given a delay system with transfer function G(s) = h2(s)h1(s), where h1(s) = ∑01npi(s) e−γis, and h2(s) = ∑02nqi(s) e−βis, with 0 = γ0< γ1 < … < γn1, 0 ⩽ β0 < … < βn2, the pi being polynomials of degree δi, and δi < δ0for i ≠ 0,and the qi polynomials of degree di < δ0 for each i, the robust stabilization of a class of perturbed coprime factors of this system is considered. Asymptotic estimates are obtained based on recent results on the approximation and stabilization of normalized coprime factors. An explicit formula is given for the normalized coprime factor stability margin for the case of a multivariable transfer function of the form G(s) = e−sTR(s), with R rational.

The Weiss conjecture on admissibility of observation operators for contraction semigroups

AbstractWe prove the conjecture of George Weiss for contraction semigroups on Hilbert spaces, giving a characterization of infinite-time admissible observation functionals for a contraction semigroup, namely that such a functionalC is infinite-time admissible if and only if there is anM>0 such that