2,821 research outputs found
Equivalence-Checking on Infinite-State Systems: Techniques and Results
The paper presents a selection of recently developed and/or used techniques
for equivalence-checking on infinite-state systems, and an up-to-date overview
of existing results (as of September 2004)
A biased approach to nonlinear robust stability and performance with applications to adaptive control
The nonlinear robust stability theory of Georgiou and Smith [IEEE Trans. Automat. Control, 42 (1997), pp. 1200–1229] is generalized to the case of notions of stability with bias terms. An example from adaptive control illustrates nontrivial robust stability certificates for systems which the previous unbiased theory could not establish a nonzero robust stability margin. This treatment also shows that the bounded-input bounded-output robust stability results for adaptive controllers in French [IEEE Trans. Automat. Control, 53 (2008), pp. 461–478] can be refined to show preservation of biased forms of stability under gap perturbations. In the nonlinear setting, it also is shown that in contrast to linear time invariant systems, the problem of optimizing nominal performance is not equivalent to maximizing the robust stability margin
Semi-groups, groups and Lyapunov stability of partial differential equations
Applications of group theory and Liapunov stability to partial differential equation
Operator synthesis II. Individual synthesis and linear operator equations
The second part of our work on operator synthesis deals with individual
operator synthesis of elements in some tensor products, in particular in
Varopoulos algebras, and its connection with linear operator equations. Using a
developed technique of ``approximate inverse intertwining'' we obtain some
generalizations of the Fuglede and the Fuglede-Weiss theorems. Additionally, we
give some applications to spectral synthesis in Varopoulos algebras and to
partial differential equations.Comment: 42 page
Reduced inequalities for vector-valued functions
Building on the notion of convex body domination introduced by Nazarov,
Petermichl, Treil, and Volberg, we provide a general principle of bootstrapping
bilinear estimates for scalar-valued functions into vector-valued versions with
a reduced right-hand side involving iterated norms of a pointwise dot product
instead of the product of lengths that would result from a na\"ive extension of the scalar inequality. On
the way, we study connections between convex body domination and tensor norms.
In order to cover the full regime of norms, also with , that
naturally arise in bilinear harmonic analysis, we develop a framework in
general quasi-normed spaces. A key application is a vector-valued Kato-Ponce
inequality (or fractional Leibnitz rule) with a reduced right-hand side, which
we obtain as a soft corollary of the known scalar-valued version and our
general bootstrapping method.Comment: 20 page
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