The Experts below are selected from a list of 13071 Experts worldwide ranked by ideXlab platform
Jong Son Shin - One of the best experts on this subject based on the ideXlab platform.
-
On stability of a class of Positive Linear Functional difference equations
Mathematics of Control Signals and Systems, 2007Co-Authors: Pham Huu Anh Ngoc, Toshiki Naito, Jong Son ShinAbstract:We first give a sufficient condition for positivity of the solution semigroup of Linear Functional difference equations. Then, we obtain a Perron–Frobenius theorem for Positive Linear Functional difference equations. Next, we offer a new explicit criterion for exponential stability of a wide class of Positive equations. Finally, we study stability radii of Positive Linear Functional difference equations. It is proved that complex, real and Positive stability radius of Positive equations under structured perturbations (or affine perturbations) coincide and can be computed by explicit formulae.
-
characterizations of Positive Linear Functional differential equations
Funkcialaj Ekvacioj, 2007Co-Authors: Pham Huu Anh Ngoc, Toshiki Naito, Jong Son ShinAbstract:In this paper, we first prove that if a Linear neutral Functional differential equation is Positive then it must degrade into a Linear Functional differential equation of retarded type. Then, we give some explicit criteria for Positive Linear Functional differential equations. Consequently, we obtain a novel criterion for exponential stability of Positive Linear Functional differential equations.
Pham Huu Anh Ngoc - One of the best experts on this subject based on the ideXlab platform.
-
On stability of a class of Positive Linear Functional difference equations
Mathematics of Control Signals and Systems, 2007Co-Authors: Pham Huu Anh Ngoc, Toshiki Naito, Jong Son ShinAbstract:We first give a sufficient condition for positivity of the solution semigroup of Linear Functional difference equations. Then, we obtain a Perron–Frobenius theorem for Positive Linear Functional difference equations. Next, we offer a new explicit criterion for exponential stability of a wide class of Positive equations. Finally, we study stability radii of Positive Linear Functional difference equations. It is proved that complex, real and Positive stability radius of Positive equations under structured perturbations (or affine perturbations) coincide and can be computed by explicit formulae.
-
characterizations of Positive Linear Functional differential equations
Funkcialaj Ekvacioj, 2007Co-Authors: Pham Huu Anh Ngoc, Toshiki Naito, Jong Son ShinAbstract:In this paper, we first prove that if a Linear neutral Functional differential equation is Positive then it must degrade into a Linear Functional differential equation of retarded type. Then, we give some explicit criteria for Positive Linear Functional differential equations. Consequently, we obtain a novel criterion for exponential stability of Positive Linear Functional differential equations.
-
stability radii of Positive Linear Functional differential equations under multi perturbations
Siam Journal on Control and Optimization, 2005Co-Authors: Pham Huu Anh Ngoc, Nguyen Khoa SonAbstract:We study stability radii of Linear retarded systems described by general Linear Functional differential equations. A lower and an upper bound for the complex stability radius with respect to multi-perturbations are given. Furthermore, in some special cases concerning the structure matrices, the complex stability radius can precisely be computed via the associated transfer function. Then, the class of Positive Linear retarded systems is studied in detail. It is shown that for this class, complex, real and Positive stability radius under multi-perturbations or multi-affine perturbations coincide and can be computed by simple formulae expressed in terms of the system matrices.
Sever S Dragomir - One of the best experts on this subject based on the ideXlab platform.
-
schwarz and gruss type inequalities for c seminorms and Positive Linear Functionals on banach modules
Linear Algebra and its Applications, 2011Co-Authors: A G Ghazanfari, Sever S DragomirAbstract:Abstract Let A be a unital Banach ∗-algebra, γ a C ∗ -seminorm or a Positive Linear Functional on A and X be a semi-inner product A -module. We define a real function Γ on X by Γ ( x ) = ( γ ( x , x > ) ) 1 / 2 and show that the Schwarz inequality holds, therefore ( X , Γ ) is a semi-Hilbert A -module. We also obtain some Gruss type inequalities for C ∗ -seminorms and Positive Linear Functionals on A .
Toshiki Naito - One of the best experts on this subject based on the ideXlab platform.
-
On stability of a class of Positive Linear Functional difference equations
Mathematics of Control Signals and Systems, 2007Co-Authors: Pham Huu Anh Ngoc, Toshiki Naito, Jong Son ShinAbstract:We first give a sufficient condition for positivity of the solution semigroup of Linear Functional difference equations. Then, we obtain a Perron–Frobenius theorem for Positive Linear Functional difference equations. Next, we offer a new explicit criterion for exponential stability of a wide class of Positive equations. Finally, we study stability radii of Positive Linear Functional difference equations. It is proved that complex, real and Positive stability radius of Positive equations under structured perturbations (or affine perturbations) coincide and can be computed by explicit formulae.
-
characterizations of Positive Linear Functional differential equations
Funkcialaj Ekvacioj, 2007Co-Authors: Pham Huu Anh Ngoc, Toshiki Naito, Jong Son ShinAbstract:In this paper, we first prove that if a Linear neutral Functional differential equation is Positive then it must degrade into a Linear Functional differential equation of retarded type. Then, we give some explicit criteria for Positive Linear Functional differential equations. Consequently, we obtain a novel criterion for exponential stability of Positive Linear Functional differential equations.
Mourrain Bernard - One of the best experts on this subject based on the ideXlab platform.
-
Computing real radicals by moment optimization
2021Co-Authors: Baldi Lorenzo, Mourrain BernardAbstract:We present a new algorithm for computing the real radical of an ideal and, more generally, the-radical of , which is based on convex moment optimization. A truncated Positive generic Linear Functional vanishing on the generators of is computed solving a Moment Optimization Problem (MOP). We show that, for a large enough degree of truncation, the annihilator of generates the real radical of. We give an e ective, general stopping criterion on the degree to detect when the prime ideals lying over the annihilator are real and compute the real radical as the intersection of real prime ideals lying over. The method involves several ingredients, that exploit the properties of generic Positive moment sequences. A new e cient algorithm is proposed to compute a graded basis of the annihilator of a truncated Positive Linear Functional. We propose a new algorithm to check that an irreducible decomposition of an algebraic variety is real, using a generic real projection to reduce to the hypersurface case. There we apply the Sign Changing Criterion, e ectively performed with an exact MOP. Finally we illustrate our approach in some examples
-
Computing real radicals by moment optimization
'Association for Computing Machinery (ACM)', 2021Co-Authors: Baldi Lorenzo, Mourrain BernardAbstract:We present a new algorithm for computing the real radical of an ideal and, more generally, the-radical of, which is based on convex moment optimization. A truncated Positive generic Linear Functional vanishing on the generators of is computed solving a Moment Optimization Problem (MOP). We show that, for a large enough degree of truncation, the annihilator of generates the real radical of. We give an effective, general stopping criterion on the degree to detect when the prime ideals lying over the annihilator are real and compute the real radical as the intersection of real prime ideals lying over. The method involves several ingredients, that exploit the properties of generic Positive moment sequences. A new efficient algorithm is proposed to compute a graded basis of the annihilator of a truncated Positive Linear Functional. We propose a new algorithm to check that an irreducible decomposition of an algebraic variety is real, using a generic real projection to reduce to the hypersurface case. There we apply the Sign Changing Criterion, effectively performed with an exact MOP. Finally we illustrate our approach in some examples.Comment: ISSAC 2021 - 46th International Symposium on Symbolic and Algebraic Computation, Jul 2021, Saint-P{\'e}tersbourg, Russi