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Jovan Stefanovski - One of the best experts on this subject based on the ideXlab platform.
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mathscr h _ infty control of descriptor systems possessing invariant zeros on the Imaginary Axis and infinity
IEEE Transactions on Automatic Control, 2015Co-Authors: Jovan StefanovskiAbstract:We present an algorithm for suboptimal ${\mathscr H}_{\infty}$ control of descriptor systems possessing invariant zeros on the Imaginary Axis and infinity. It is proved that the algorithm works also in an optimality case. The algorithm is illustrated by examples.
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${\mathscr H}_{\infty}$ Control of Descriptor Systems Possessing Invariant Zeros on the Imaginary Axis and Infinity
IEEE Transactions on Automatic Control, 2015Co-Authors: Jovan StefanovskiAbstract:We present an algorithm for suboptimal ${\mathscr H}_{\infty}$ control of descriptor systems possessing invariant zeros on the Imaginary Axis and infinity. It is proved that the algorithm works also in an optimality case. The algorithm is illustrated by examples.
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Optimal boundary interpolation and one-block optimal control problem with invariant zeros on the Imaginary Axis and infinity
International Journal of Control, 2014Co-Authors: Jovan StefanovskiAbstract:We formulate a matrix interpolation problem with existing interpolation points on the Imaginary Axis and infinity and existing equal left and right interpolation points, using the concept of parametrisation of stabilising controllers. Then, we solve the problem of obtaining all its solutions. If interpolation points at infinity are absent, we show that the introduced problem is equivalent to the existing one. We apply this result to solve the problem of optimal interpolation with existent interpolation points on the Imaginary Axis and infinity. We show by an example that the solution of optimal interpolation is directly applicable to the one-block optimal control with existent invariant zeros on the Imaginary Axis and infinity. It is seen from the example that not only the transfer matrix of the closed-loop system is constrained on the extended Imaginary Axis, but also its derivatives.
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Algorithms for optimal control with invariant zeros on the extended Imaginary Axis
Systems & Control Letters, 2013Co-Authors: Jovan StefanovskiAbstract:Abstract We transform an ℋ ∞ control problem with invariant zeros on the extended Imaginary Axis into a regular problem. Then using the Nevanlinna–Pick theorem, we find necessary and sufficient existence conditions for the original ℋ ∞ control problem. An algorithm and examples with invariant zeros on the extended Imaginary Axis are given. By the same approach, we also solve the singular ℋ 2 control problem.
Takaaki Nishida - One of the best experts on this subject based on the ideXlab platform.
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traveling waves bifurcating from plane poiseuille flow of the compressible navier stokes equation
Archive for Rational Mechanics and Analysis, 2019Co-Authors: Yoshiyuki Kagei, Takaaki NishidaAbstract:Plane Poiseuille flow in viscous compressible fluid is known to be asymptotically stable if Reynolds number R and Mach number M are sufficiently small. On the other hand, for R and M being not necessarily small, an instability criterion for plane Poiseuille flow is known, and the criterion says that, when R increases, a pair of complex conjugate eigenvalues of the linearized operator cross the Imaginary Axis. In this paper it is proved that a spatially periodic traveling wave bifurcates from plane Poiseuille flow when the critical eigenvalues cross the Imaginary Axis.
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Traveling Waves Bifurcating from Plane Poiseuille Flow of the Compressible Navier–Stokes Equation
Archive for Rational Mechanics and Analysis, 2018Co-Authors: Yoshiyuki Kagei, Takaaki NishidaAbstract:Plane Poiseuille flow in viscous compressible fluid is known to be asymptotically stable if Reynolds number R and Mach number M are sufficiently small. On the other hand, for R and M being not necessarily small, an instability criterion for plane Poiseuille flow is known, and the criterion says that, when R increases, a pair of complex conjugate eigenvalues of the linearized operator cross the Imaginary Axis. In this paper it is proved that a spatially periodic traveling wave bifurcates from plane Poiseuille flow when the critical eigenvalues cross the Imaginary Axis.
Catherine Bonnet - One of the best experts on this subject based on the ideXlab platform.
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Stabilizability of Some Neutral Delay Systems with Chains of Poles Clustering on the Imaginary Axis
2016Co-Authors: Catherine Bonnet, Yutaka YamamotoAbstract:When dealing with phenomena such as transport, propagation or communication, it is a crucial issue to take delays into account to avoid bad performances. Neutral type delay systems are the most delicate to analyze as they may have chains of poles clustering the Imaginary Axis. We investigate here the Hinfinity-stabilizability of two particular neutral delay systems with a chain of poles clustering the Imaginary Axis: the first one having a chain of poles in the left-half plane and the second one having a chain of poles in the right-half plane. In both case, we show how to construct a coprime factorization over Hinfinity proving then they are both Hinfinity-stabilizable.
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Hinfty-stability analysis of various classes of neutral time-delay systems with chains of poles approching the Imaginary Axis
2015Co-Authors: Le Ha Vy Nguyen, Catherine BonnetAbstract:We analyze the H∞-stability of neutral systems with commensurate delays and multiple chains of poles asymptotic to a same set of points on the Imaginary Axis. First, by approximation, the location of poles of large modulus is determined. This analysis requires to consider several subclasses of systems where poles of high modulus exhibit various patterns. Second, we derive necessary and sufficient conditions for H∞-stability which are easy to check as expressed in terms of the degrees of the polynomials involved in the numerator and denominator of the transfer function.
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h stability analysis of various classes of neutral systems with commensurate delays and with chains of poles approaching the Imaginary Axis
Conference on Decision and Control, 2015Co-Authors: Le Ha Vy Nguyen, Catherine BonnetAbstract:We analyze the H∞-stability of neutral systems with commensurate delays and multiple chains of poles asymptotic to a same set of points on the Imaginary Axis. First, by approximation, the location of poles of large modulus is determined. This analysis requires to consider several subclasses of systems where poles of high modulus exhibit various patterns. Second, we derive necessary and sufficient conditions for H∞-stability which are easy to check as expressed in terms of the degrees of the polynomials involved in the numerator and denominator of the transfer function.
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H-infinity-stability analysis of various classes of neutral systems with commensurate delays and with chains of poles approaching the Imaginary Axis
2015Co-Authors: Le Ha Vy Nguyen, Catherine BonnetAbstract:We analyze the H-infinity-stability of neutral systems with commensurate delays and multiple chains of poles asymptotic to a same set of points on the Imaginary Axis. First, by approximation, the location of poles of large modulus is determined. This analysis requires to consider several subclasses of systems where poles of high modulus exhibit various patterns. Second, we derive necessary and sufficient conditions for H-infinity-stability which are easy to check as expressed in terms of the degrees of the polynomials involved in the numerator and denominator of the transfer function.
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CDC - H∞-stability analysis of various classes of neutral systems with commensurate delays and with chains of poles approaching the Imaginary Axis
2015 54th IEEE Conference on Decision and Control (CDC), 2015Co-Authors: Le Ha Vy Nguyen, Catherine BonnetAbstract:We analyze the H∞-stability of neutral systems with commensurate delays and multiple chains of poles asymptotic to a same set of points on the Imaginary Axis. First, by approximation, the location of poles of large modulus is determined. This analysis requires to consider several subclasses of systems where poles of high modulus exhibit various patterns. Second, we derive necessary and sufficient conditions for H∞-stability which are easy to check as expressed in terms of the degrees of the polynomials involved in the numerator and denominator of the transfer function.
Yoshiyuki Kagei - One of the best experts on this subject based on the ideXlab platform.
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traveling waves bifurcating from plane poiseuille flow of the compressible navier stokes equation
Archive for Rational Mechanics and Analysis, 2019Co-Authors: Yoshiyuki Kagei, Takaaki NishidaAbstract:Plane Poiseuille flow in viscous compressible fluid is known to be asymptotically stable if Reynolds number R and Mach number M are sufficiently small. On the other hand, for R and M being not necessarily small, an instability criterion for plane Poiseuille flow is known, and the criterion says that, when R increases, a pair of complex conjugate eigenvalues of the linearized operator cross the Imaginary Axis. In this paper it is proved that a spatially periodic traveling wave bifurcates from plane Poiseuille flow when the critical eigenvalues cross the Imaginary Axis.
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Traveling Waves Bifurcating from Plane Poiseuille Flow of the Compressible Navier–Stokes Equation
Archive for Rational Mechanics and Analysis, 2018Co-Authors: Yoshiyuki Kagei, Takaaki NishidaAbstract:Plane Poiseuille flow in viscous compressible fluid is known to be asymptotically stable if Reynolds number R and Mach number M are sufficiently small. On the other hand, for R and M being not necessarily small, an instability criterion for plane Poiseuille flow is known, and the criterion says that, when R increases, a pair of complex conjugate eigenvalues of the linearized operator cross the Imaginary Axis. In this paper it is proved that a spatially periodic traveling wave bifurcates from plane Poiseuille flow when the critical eigenvalues cross the Imaginary Axis.
Masato Tsujii - One of the best experts on this subject based on the ideXlab platform.
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The semiclassical zeta function for geodesic flows on negatively curved manifolds
Inventiones mathematicae, 2017Co-Authors: Frédéric Faure, Masato TsujiiAbstract:We consider the semi-classical (or Gutzwiller–Voros) zeta functions for $$C^\infty $$ C ∞ contact Anosov flows. Analyzing the spectra of the generators of some transfer operators associated to the flow, we prove that, for arbitrarily small $$\tau >0$$ τ > 0 , its zeros are contained in the union of the $$\tau $$ τ -neighborhood of the Imaginary Axis, $$|\mathfrak {R}(s)| 0 is the hyperbolicity exponent of the flow. Further we show that the density of the zeros along the Imaginary Axis satisfy an analogue of the Weyl law.
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The semiclassical zeta function for geodesic flows on negatively curved manifolds
arXiv: Dynamical Systems, 2013Co-Authors: Frédéric Faure, Masato TsujiiAbstract:We consider the semi-classical (or Gutzwiller-Voros) zeta function for $C^\infty$ contact Anosov flows. Analyzing the spectrum of transfer operators associated to the flow, we prove, for any $\tau>0$, that its zeros are contained in the union of the $\tau$-neighborhood of the Imaginary Axis, $|\Re(s)| 0$ is the hyperbolicity exponent of the flow. Further we show that the zeros in the neighborhood of the Imaginary Axis satisfy an analogue of the Weyl law.
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Spectrum of geodesic flow on negatively curved manifold
2013Co-Authors: Masato TsujiiAbstract:We consider the one-parameter families of transfer operators for geodesic flows on negatively curved manifolds. We show that the spectra of the generators have some "band structure" parallel to the Imaginary Axis. As a special case of "semi-classical" transfer operator, we see that the eigenvalues concentrate around the Imaginary Axis with some gap on the both sides.