George Zames

Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses

In this paper, the problem of sensitivity, reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization. Stable feedback schemes obtainable from a given plant are parameterized. Salient properties of sensitivity reducing schemes are derived, and it is shown that plant uncertainty reduces the ability, of feedback to reduce sensitivity. The theory is developed for input-output systems in a general setting of Banach algebras, and then specialized to a class of multivariable, time-invariant systems characterized by n \times n matrices of H^{\infty} frequency response functions, either with or without zeros in the right half-plane. The approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity, and on the concept of an approximate inverse. Approximate invertibility, of the plant is shown to be a necessary and sufficient condition for sensitivity reduction. An indicator of approximate invertibility, called a measure of singularity, is introduced. The measure of singularity of a linear time-invariant plant is shown to be determined by the location of its right half-plane zeros. In the absence of plant uncertainty, the sensitivity, to output disturbances can be reduced to an optimal value approaching the singularity, measure. In particular, if there are no right half-plane zeros, sensitivity can be made arbitrarily small. The feedback schemes used in the optimization of sensitivity resemble the lead-lag networks of classical control design. Some of their properties, and methods of constructing them in special cases are presented.

On the metric complexity of casual linear systems: ε -Entropy and ε -Dimension for continuous time

Estimates of e-entropy and e-dimension in the Kolmogorov sense are obtained for a class of causal, linear, time-invariant, continuous-time systems under the assumptions that impulse responses, satisfy an exponential order condition |f(t)| \leq Ce ^{-at} , and frequency responses satisfy an attenuation condition |F(j\omega)|\leg K\omega^{-1} . The dependence of e-entropy and e-dimension on the accuracy e is characterized by order, type, and power indexes. Similar results for the discrete-time case are reviewed and compared.

Weighted sensitivity minimization for delay systems

In this note we discuss the H¿-sensitivity minimitization problem for linear time-invariant delay systems. While the unweighted case reduces to simple Nevanlinna-Pick interpolation, the weighted case turns out to be much more complicated and demands certain functional - analytic techniques for its solution.

Dither in nonlinear systems

A dither is a high-frequency signal introduced into a nonlinear system with the object of augmenting stability. In this paper,[1] it is shown that the effects of dither depend on its amplitude distribution function. The stability of a dithered system is related to that of an equivalent smoothed system, whose nonlinear element is the convolution of the dither distribution and the original nonlinearity. The ability of dithers to stabilize large classes of nonlinear systems is explained in terms of an effective narrowing of the nonlinear sector. A feature of the approach taken here is that a deterministic (i.e., strong) concept of stability is established under probabilistic (i.e., weak) assumptions on the dither.

Some Explicit Formulae for the Singular Values of Certain Hankel Operators with Factorizable Symbol

In this paper a determinantal formula is written that allows one to compute the singular values of Hankel operators, the

On the H ∞ -optimal sensitivity problem for systems with delays

L^\infty

Fast identification n-widths and uncertainty principles for LTI and slowly varying systems

-symbols of which are of the form

Local-global double algebras for slow H/sup infinity / adaptation. I. Inversion and stability

\bar mw

A note on essential spectra and norms of mixed Hankel-Toeplitz operators

for

Duality theory for MIMO robust disturbance rejection

w \in H^\infty