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Y. Genin

Bio: Y. Genin is an academic researcher from Université catholique de Louvain. The author has contributed to research in topics: Matrix polynomial & Stability radius. The author has an hindex of 7, co-authored 15 publications receiving 257 citations.

Papers
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TL;DR: A unifying framework is revealed where several known results fit naturally and special attention is given to the embedding problem of the Lyapunov equation in view of its direct application to generalized Levinson algorithms.

104 citations

Journal ArticleDOI
TL;DR: In this article, the complex and real stability radii of non-monic polynomial matrices with respect to an arbitrary stability region of the complex plane were derived for different perturbation structures.

32 citations

Journal ArticleDOI
TL;DR: This paper uses the general theory of Popov realizations of parahermitian transfer functions in the context of generalized state space systems to derive linear matrix inequalities for some particular applications in systems and control.

32 citations

Journal ArticleDOI
TL;DR: In this paper, a generalized Routh-Hurwitz algorithm is proposed, which allows one to determine, in any situation, the numbers of zeros of an arbitrary complex polynomial in the right half plane, on the imaginary axis, and hence in the left half plane.

19 citations


Cited by
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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: A necessary and sufficient condition for an S-procedure to be lossless is developed, and the result is used to generalize the KYP lemma in two aspects-the frequency range and the class of systems-and to unify various existing versions by a single theorem.
Abstract: The celebrated Kalman-Yakubovic/spl caron/-Popov (KYP) lemma establishes the equivalence between a frequency domain inequality (FDI) and a linear matrix inequality, and has played one of the most fundamental roles in systems and control theory. This paper first develops a necessary and sufficient condition for an S-procedure to be lossless, and uses the result to generalize the KYP lemma in two aspects-the frequency range and the class of systems-and to unify various existing versions by a single theorem. In particular, our result covers FDIs in finite frequency intervals for both continuous/discrete-time settings as opposed to the standard infinite frequency range. The class of systems for which FDIs are considered is no longer constrained to be proper, and nonproper transfer functions including polynomials can also be treated. We study implications of this generalization, and develop a proper interface between the basic result and various engineering applications. Specifically, it is shown that our result allows us to solve a certain class of system design problems with multiple specifications on the gain/phase properties in several frequency ranges. The method is illustrated by numerical design examples of digital filters and proportional-integral-derivative controllers.

955 citations

01 Jan 2000
TL;DR: The present book intends to describe the current state of this approach to ~® control, the so-called time domain or state space methods which were developed in the late 1980s.
Abstract: DURING THE LAST DECADE, much attention has been drawn to control theory especially as an approach to robust compensator design. In the past years a huge number of scientific publications, and among these several monographies, were published on this and related subjects. In the late 1980s there was a breakthrough in ~t~® control theory, the so-called time domain or state space approach, which gave very elegant results leading to simple design techniques. There has since been a demand for a thorough textbook to describe these new methods in detail. control theory originated in the early 1980s where the control community had been aware for some time of the poor robustness properties of classical observer-based controller methods and LQG design. This led to the formulation of the robust stability problem which was intensely studied in the following years. There were several approaches which lead to solutions of this problem. These were based on frequency domain methods and transfer function descriptions as presented in Francis (1987). Later on, the significance of ~i~® control theory to a wide variety of control problems such as for example loop shaping became apparent, since the ~g'~ methods are well suited to treat a rather general class of design problems with frequency domain specifications. However, the widespread popularity that ~® has attained today is mainly due to a more recent development, namely the time domain or state space methods which were developed in the late 1980s. In this line of research it became evident that solvability of the so-called ~C® standard problem (which comprises the robust stability problem and several other problems as special cases) is equivalent to solvability of two algebraic Riccati equations and a coupling condition. Moreover, a complete characterization of the whole class of solutions to the ~ control problem was obtained in closed form. The present book intends to describe the current state of this approach to ~® control. In the introductory part of the book the deficiencies of classical control with respect to robustness issues are pointed out, and the ~® control problem is introduced. It is shown, however, by means of an example that a solution to the ~ control problem does not necessarily have good stability margins. Hence, it is emphasized that the formulation of the control problem itself does not guarantee robustness. Robustness is obtained only if it designed for! The robustness issue is further addressed as stabilization of uncertain systems and as graph topology convergence, and the mixed sensitivity problem is introduced as an approach to the nominal performance/robust stability problem. The exposition given in the book requires a number of mathematical prerequisties which are collected in a separate chapter. Among these are: properties of linear continuous or discrete time systems, theory for rational matrices and theory

249 citations

Book
30 Jun 1998
TL;DR: In this article, the authors present an overview of the history of non-uniform spaces in the Hilbert space, including inner-outer and inner-outer factorization, J-Unitary operators, and lossless Cascade Factorization.
Abstract: Preface. 1. Introduction. Part I: Realization. 2. Notation and Properties of Non-Uniform Spaces. 3. Time-Varying State Space Realizations. 4. Diagonal Algebra. 5. Operator Realization Theory. 6. Isometric and Inner Operators. 7. Inner-Outer Factorization and Operator Inversion. Part II: Interpolation and Approximation. 8. J-Unitary Operators. 9. Algebraic Interpolation. 10. Hankel-Norm Model Reduction. 11. Low-Rank Matrix Approximation and Subspace Tracking. Part III: Factorization. 12. Orthogonal Embedding. 13. Spectral Factorization. 14. Lossless Cascade Factorizations. 15. Conclusions. Appendices: A. Hilbert Space Definitions and Properties. References. Glossary of Notation. Index.

225 citations