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Wavelet transform for time-frequency representation and filtration of discrete signals

Waldemar Popiński (1996)

Applicationes Mathematicae

A method to analyse and filter real-valued discrete signals of finite duration s(n), n=0,1,...,N-1, where N = 2 p , p>0, by means of time-frequency representation is presented. This is achieved by defining an invertible discrete transform representing a signal either in the time or in the time-frequency domain, which is based on decomposition of a signal with respect to a system of basic orthonormal discrete wavelet functions. Such discrete wavelet functions are defined using the Meyer generating wavelet...

Wavelets on fractals.

Dorin E. Dutkay, Palle E.T. Jorgensen (2006)

Revista Matemática Iberoamericana

We show that there are Hilbert spaces constructed from the Hausdorff measures Hs on the real line R with 0 < s < 1 which admit multiresolution wavelets. For the case of the middle-third Cantor set C ⊂ [0,1], the Hilbert space is a separable subspace of L2(R, (dx)s) where s = log3(2). While we develop the general theory of multiresolutions in fractal Hilbert spaces, the emphasis is on the case of scale 3 which covers the traditional Cantor set C.

Weak and exact domination in distributed systems

Larbi Afifi, El Mostafa Magri, Abdelhaq El Jai (2010)

International Journal of Applied Mathematics and Computer Science

In this work, we introduce and examine the notion of domination for a class of linear distributed systems. This consists in studying the possibility to make a comparison between input or output operators. We give the main algebraic properties of such relations, as well as characterizations of exact and weak domination. We also study the case of actuators, and various situations are examined. Applications and illustrative examples are also given. By duality, we extend this study to observed systems....

Weak regularizability and pole assignment for non-square linear systems

Tetiana Korotka, Jean-Jacques Loiseau, Petr Zagalak (2012)

Kybernetika

The problem of pole assignment by state feedback in the class of non-square linear systems is considered in the paper. It is shown that the problem is solvable under the assumption of weak regularizability, a newly introduced concept that can be viewed as a generalization of the regularizability of square systems. Necessary conditions of solvability for the problem of pole assignment are established. It is also shown that sufficient conditions can be derived in some special cases. Some conclusions...

Weak solutions of stochastic differential inclusions and their compactness

Mariusz Michta (2009)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we consider weak solutions to stochastic inclusions driven by a semimartingale and a martingale problem formulated for such inclusions. Using this we analyze compactness of the set of solutions. The paper extends some earlier results known for stochastic differential inclusions driven by a diffusion process.

Weak structure at infinity and row-by-row decoupling for linear delay systems

Rabah Rabah, Michel Malabre (2004)

Kybernetika

We consider the row-by-row decoupling problem for linear delay systems and show some close connections between the design of a decoupling controller and some particular structures of delay systems, namely the so-called weak structure at infinity. The realization by static state feedback of decoupling precompensators is studied, in particular, generalized state feedback laws which may incorporate derivatives of the delayed new reference.

Weighted ℋ ∞ mixed-sensitivity minimization for stable distributed parameter plants under sampled data control

Delano R. Carter, Armando A. Rodriguez (1999)

Kybernetika

This paper considers the problem of designing near-optimal finite-dimensional controllers for stable multiple-input multiple-output (MIMO) distributed parameter plants under sampled-data control. A weighted ℋ ∞ -style mixed-sensitivity measure which penalizes the control is used to define the notion of optimality. Controllers are generated by solving a “natural” finite-dimensional sampled-data optimization. A priori computable conditions are given on the approximants such that the resulting finite-...

Well-formed dynamics under quasi-static state feedback

J. Rudolph (1995)

Banach Center Publications

Well-formed dynamics are a generalization of classical dynamics, to which they are equivalent by a quasi-static state feedback. In case such a dynamics is flat, i.e., equivalent by an endogenous feedback to a linear controllable dynamics, there exists a Brunovský type canonical form with respect to a quasi-static state feedback.

Well-posed linear systems - a survey with emphasis on conservative systems

George Weiss, Olof Staffans, Marius Tucsnak (2001)

International Journal of Applied Mathematics and Computer Science

We survey the literature on well-posed linear systems, which has been an area of rapid development in recent years. We examine the particular subclass of conservative systems and its connections to scattering theory. We study some transformations of well-posed systems, namely duality and time-flow inversion, and their effect on the transfer function and the generating operators. We describe a simple way to generate conservative systems via a second-order differential equation in a Hilbert space....

Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain

Hans Zwart, Yann Le Gorrec, Bernhard Maschke, Javier Villegas (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We study a class of hyperbolic partial differential equations on a one dimensional spatial domain with control and observation at the boundary. Using the idea of feedback we show these systems are well-posed in the sense of Weiss and Salamon if and only if the state operator generates a C0-semigroup. Furthermore, we show that the corresponding transfer function is regular, i.e., has a limit for s going to infinity.

Well-posedness and sliding mode control

Tullio Zolezzi (2005)

ESAIM: Control, Optimisation and Calculus of Variations

Sliding mode control of ordinary differential equations is considered. A key robustness property, called approximability, is studied from an optimization point of view. It is proved that Tikhonov well-posedness of a suitably defined optimization problem is intimately related to approximability. Making use of this link, new approximability criteria are obtained for nonlinear sliding mode control systems.

Well-posedness and sliding mode control

Tullio Zolezzi (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Sliding mode control of ordinary differential equations is considered. A key robustness property, called approximability, is studied from an optimization point of view. It is proved that Tikhonov well-posedness of a suitably defined optimization problem is intimately related to approximability. Making use of this link, new approximability criteria are obtained for nonlinear sliding mode control systems.

Weyl formula with optimal remainder estimate of some elastic networks and applications

Kaïs Ammari, Mouez Dimassi (2010)

Bulletin de la Société Mathématique de France

We consider a network of vibrating elastic strings and Euler-Bernoulli beams. Using a generalized Poisson formula and some Tauberian theorem, we give a Weyl formula with optimal remainder estimate. As a consequence we prove some observability and stabilization results.

What is not clear in fuzzy control systems

Andrzej Piegat (2006)

International Journal of Applied Mathematics and Computer Science

The paper presents a number of unclear, unsolved or partly solved problems of fuzzy logic, which hinder precise transformation of expert knowledge about proper control of a plant in a fuzzy controller. These vague problems comprise the realization of logical and arithmetic operations and another basic problem, i.e., the construction of membership functions. The paper also indicates how some of the above problems can be solved.

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