We introduce and study problems of distributed observation with bounded or unbounded memory. We are given a system modeled as a finite-word language L over some finite alphabet Σ and subalphabets Σ1, ...,Σn of Σ modeling n distinct observation points. We want to build (when there exist) n observers which collect projections of a behavior in L onto Σ1, ...,Σn, then send them to a central decisio...

Let L be a linear space of real bounded random variables on the probability space (Ω,A, P0). A finitely additive probability P on A such that P ∼ P0 and EP (X) = 0 for each X ∈ L is called EMFA (equivalent martingale finitely additive probability). In this note, EMFA’s are investigated in case P0 is atomic. Existence of EMFA’s is characterized and various examples are given. Given y ∈ R and a b...

The purpose of this paper is to describe systematic analysis and design tools for robust control problems with l∞ criteria. We first generalize the Hill-MoylanWillems framework for dissipative systems to accommodate l∞ criteria, and then derive state feedback and measurement feedback synthesis procedures for l∞ robust control problems. The information state framework is used for the measurement...

A version of nonlinear generalization of the C1-control problem, which deals with the attenuation of persistent bounded disturbances in &-sense, is investigated in this paper. The methods used in this paper are motivated by [23]. The main idea in the C1-performance analysis and synthesis is to construct a certain invariant subset of the state-space such that achieving disturbance rejection is e...

A connection is established between uniform rational approximation and approximation in the mean by polynomials on compact nowhere dense subsets of the complex plane C. Peak points for R(X) and bounded point evaluations for Hp(X, dA), 1 ≤ p < ∞, play a fundamental role.

We use the method of Scholz and Reichardt and a transfer principle from finite fields to pseudo finite fields in order to prove the following result. Theorem: Let G be a group of order l, where l is a prime number. Let K0 be either a finite field with |K0| > l or a pseudo finite field. Suppose that l 6= char(K0) and that K0 does not contain the root of unity ζl of order l. Let K = K0(t), with t...

It is important to study asymptotic behavior of complete manifold without the assumption of pointwise Ricci curvature bound. A volume growth and curvature decay result was obtained in [4] for various classes of complete, noncompact, Bach-flat metrics in dimension 4. Some similar results were also claimed in [1]. In this note we consider a more general case, that is, the Bach tensor may not nece...

In this paper we solve a measurement feedback disturbance rejection robust control problem for nonlinear systems based on a l∞ criterion. Information state techniques are employed to obtain necessary and sufficient conditions, and a controller synthesis procedure. The results are consistent with the separation structure in Shamma-Tu (1999).

We modify the definition of l-homology and argue why our definition is more adequate than the classical one. While we cannot reconstruct the classical l-homology from the new definition for various reasons, we can reconstruct its Hausdorffification so that no information concerning semi-norms is lost. We obtain an axiomatic characterization of our l-homology as a universal δ-functor and prove t...

In this paper, we consider the L∞-bounded robust control problem for a class of nonlinear cascade systems with disturbances. Sufficient conditions are provided under which a hard bound is imposed on the system performance measure. The backstepping approach is used for controller design. Examples are provided to illustrate the method. Key-words. Nonlinear cascade systems, L∞ bound, robust contro...