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Jaroslav Kautsky

Bio: Jaroslav Kautsky is an academic researcher from Flinders University. The author has contributed to research in topics: Orthogonal polynomials & Matrix (mathematics). The author has an hindex of 19, co-authored 48 publications receiving 2273 citations.

Papers
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Journal ArticleDOI
TL;DR: This paper investigates the reasons for these instabilities in three particular cases-central moments, complex moments, and moment blur invariants and shows that they can be partially overcome by choosing an appropriate polynomial basis.

3 citations

01 Jan 1983
TL;DR: In this article, the authors describe algorithms for computing solutions to the pole assignment problem which satisfy certain robustness criteria, which guarantee that the assi~ned eigenvalues are as insensitive to perturbations as is feasible, and also that the resulting feedback matrix and corresponding transient response are as reasonably bounded as may be expected, given the original system.
Abstract: design is essentially an inverse eigenvalue problem, which requires the determination of a matrix having given eigenvalues (cf. Fletcher, in these proceedings). A number of formally constructive methods for eigenvalue assignment by feedback are described in the literature ,13J OlJ, 11 J, but these procedures are not in general stable for numerical computation, and do not necessarily lead to robust, or well-conditioned, solutions of the problem, that is, to solutions which are insensitive to perturbations in the system. Stable numerical methods for inverse eigenvalue problems have been developed in other contexts (compare for instance, references '2], '5J, [6J), but these procedures are desi~ned to handle only very specific classes of matrices and are not directly applicable to the forms arising in control theory. The basic difficulty in develoning an algorithm for the inverse eigenvalue problem is that the solution is not uniquely determined. In the special case of a single-input control system, only one solution to the eigenvalue assignment problem may exist, and a numeri­ cally stable technique for computing the feedback is available [9l. For the nUlti-input problem additional criteria must be imposed to restrict the degrees of freedom in the problem. In this paper we describe algorithms for computing solutions to the pole assignment problem which satisfy certain robustness criteria. These criteria guarantee that the assi~ned eigenvalues are as insensitive to pertur­ bations as is feasible, and also that the resulting feedback matrix and corresponding transient response are as reasonably bounded as may be expected, given the original system. In the next section the pole assignment problem is defined in detail, and theoretical considerations are discussed. In Section 3 we describe the numerical al~orithm.

1 citations

Journal ArticleDOI
TL;DR: In this article , the authors introduce new rotation moment invariants, which are composed of non-separable Appell moments and prove that Appell polynomials behave under rotation as monomials, which enables easy construction of the invariants.

1 citations

Proceedings ArticleDOI
06 Apr 1995
TL;DR: In this article, the convergence of the cascade algorithm and sufficient conditions for existence of solution to a two-scale dilation equation were derived for multiresolution analysis with block Toeplitz-like operators.
Abstract: Because multiresolution analyses and wavelet bases are generated by translating and dilating scaling and wavelet functions, these functions must satisfy some special equations involving Toeplitz and Toeplitz-like operations. These relations can be exploited when such functions are to be constructed or their properties are studied. In the case of multiwavelets, where more than one scaling functions generate the multiresolution analysis, the corresponding operators are block Toeplitz-like. We discuss here some basic properties of these operators and compare them to the classical case of one scaling function. Using these observations we study the convergence of the cascade algorithm and derive sufficient conditions for existence of solution to a two-scale dilation equation.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

1 citations


Cited by
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Journal ArticleDOI
TL;DR: A review of recent as well as classic image registration methods to provide a comprehensive reference source for the researchers involved in image registration, regardless of particular application areas.

6,842 citations

Book
27 Sep 2011
TL;DR: Robust Model-Based Fault Diagnosis for Dynamic Systems targets both newcomers who want to get into this subject, and experts who are concerned with fundamental issues and are also looking for inspiration for future research.
Abstract: There is an increasing demand for dynamic systems to become safer and more reliable This requirement extends beyond the normally accepted safety-critical systems such as nuclear reactors and aircraft, where safety is of paramount importance, to systems such as autonomous vehicles and process control systems where the system availability is vital It is clear that fault diagnosis is becoming an important subject in modern control theory and practice Robust Model-Based Fault Diagnosis for Dynamic Systems presents the subject of model-based fault diagnosis in a unified framework It contains many important topics and methods; however, total coverage and completeness is not the primary concern The book focuses on fundamental issues such as basic definitions, residual generation methods and the importance of robustness in model-based fault diagnosis approaches In this book, fault diagnosis concepts and methods are illustrated by either simple academic examples or practical applications The first two chapters are of tutorial value and provide a starting point for newcomers to this field The rest of the book presents the state of the art in model-based fault diagnosis by discussing many important robust approaches and their applications This will certainly appeal to experts in this field Robust Model-Based Fault Diagnosis for Dynamic Systems targets both newcomers who want to get into this subject, and experts who are concerned with fundamental issues and are also looking for inspiration for future research The book is useful for both researchers in academia and professional engineers in industry because both theory and applications are discussed Although this is a research monograph, it will be an important text for postgraduate research students world-wide The largest market, however, will be academics, libraries and practicing engineers and scientists throughout the world

3,826 citations

Book
14 Aug 1997
TL;DR: This work describes the development of the Basic Multiresolution Wavelet System and some of its components, as well as some of the techniques used to design and implement these systems.
Abstract: 1 Introduction to Wavelets 2 A Multiresolution Formulation of Wavelet Systems 3 Filter Banks and the Discrete Wavelet Transform 4 Bases, Orthogonal Bases, Biorthogonal Bases, Frames, Tight Frames, and Unconditional Bases 5 The Scaling Function and Scaling Coefficients, Wavelet and Wavelet Coefficients 6 Regularity, Moments, and Wavelet System Design 7 Generalizations of the Basic Multiresolution Wavelet System 8 Filter Banks and Transmultiplexers 9 Calculation of the Discrete Wavelet Transform 10 Wavelet-Based Signal Processing and Applications 11 Summary Overview 12 References Bibliography Appendix A Derivations for Chapter 5 on Scaling Functions Appendix B Derivations for Section on Properties Appendix C Matlab Programs Index

2,339 citations

Journal ArticleDOI
TL;DR: This work surveys the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques.
Abstract: We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting both the structure of the matrices in the problem (dense, sparse, real, complex, Hermitian, skew-Hermitian) and the spectral properties of the problem. We classify numerical methods and catalogue available software.

1,369 citations

Journal ArticleDOI
TL;DR: Numerical methods are described for determining robust, or well-conditioned, solutions to the problem of pole assignment by state feedback such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized.
Abstract: Numerical methods are described for determining robust, or well-conditioned, solutions to the problem of pole assignment by state feedback. The solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized. It is shown that for these solutions, upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized. A measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed-loop poles, and hence the suitability of the given poles for assignment.

1,035 citations