Connection between the spectral problem for linear matrix pencils and some problems of algebra

1985 ◽  
Vol 28 (3) ◽  
pp. 341-353
Author(s):  
V. N. Kublanovskaya
Keyword(s):  
Spectral Problem ◽  
Linear Matrix ◽  
Matrix Pencils

Pseudospectra of linear matrix pencils by block diagonalization

Computing ◽  
1998 ◽  
Vol 60 (2) ◽  
pp. 133-156 ◽  
Author(s):  
P.-F. Lavallée ◽  
M. Sadkane
Keyword(s):  
Linear Matrix ◽  
Block Diagonalization ◽  
Matrix Pencils

A Newton-type method for non-linear eigenproblems

2017 ◽  
Vol 32 (4) ◽  
Author(s):  
Kirill V. Demyanko ◽  
Yuri M. Nechepurenko ◽  
Miloud Sadkane
Keyword(s):  
Stability Problem ◽  
Linear Matrix ◽  
Type Method ◽  
Spatial Stability ◽  
Non Linear ◽  
Matrix Pencils ◽  
Linear Problems ◽  
Partial Linear

AbstractThis work is devoted to computations of invariant pairs associated with separated groups of finite eigenvalues of large regular non-linear matrix pencils. It is proposed to combine the method of successive linear problems with a Newton-type method designed for partial linear eigenproblems and a deflation procedure. This combination is illustrated with a typical hydrodynamic spatial stability problem.

scholarly journals Hilbert’s 17th problem in free skew fields

2020 ◽  
Vol 9 ◽  
Author(s):  
Jurij Volčič
Keyword(s):  
Rational Function ◽  
Extension Theorem ◽  
Rational Functions ◽  
Positive Semidefinite ◽  
Linear Matrix ◽  
Intermediate Step ◽  
Noncommutative Polynomials ◽  
Skew Fields ◽  
Matrix Pencils ◽  
17Th Problem

Abstract This paper solves the rational noncommutative analogue of Hilbert’s 17th problem: if a noncommutative rational function is positive semidefinite on all tuples of Hermitian matrices in its domain, then it is a sum of Hermitian squares of noncommutative rational functions. This result is a generalisation and culmination of earlier positivity certificates for noncommutative polynomials or rational functions without Hermitian singularities. More generally, a rational Positivstellensatz for free spectrahedra is given: a noncommutative rational function is positive semidefinite or undefined at every matricial solution of a linear matrix inequality $L\succeq 0$ if and only if it belongs to the rational quadratic module generated by L. The essential intermediate step toward this Positivstellensatz for functions with singularities is an extension theorem for invertible evaluations of linear matrix pencils.

A block Newton’s method for computing invariant pairs of nonlinear matrix pencils

2018 ◽  
Vol 33 (1) ◽  
pp. 15-23
Author(s):  
Kirill V. Demyanko ◽  
Yuri M. Nechepurenko
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Linear Matrix ◽  
Inverse Iteration ◽  
Matrix Pencils ◽  
Nonlinear Matrix ◽  
Newton's Methods

Abstract The block inverse iteration and block Newton’s methods proposed by the authors of this paper for computing invariant pairs of regular linear matrix pencils are generalized to the case of regular nonlinear matrix pencils. Numerical properties of the proposed methods are demonstrated with a typical quadratic eigenproblem.

Robust H2 Output Feedback Controller Design for Damping Power System Oscillations

2017 ◽  
Vol 6 (10) ◽  
pp. 8
Author(s):  
Kho Hie Kwee ◽  
Hardiansyah .
Keyword(s):  
Power System ◽  
Output Feedback ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Worst Case ◽  
Output Feedback Controller ◽  
Power System Oscillations

This paper addresses the design problem of robust H2 output feedback controller design for damping power system oscillations. Sufficient conditions for the existence of output feedback controllers with norm-bounded parameter uncertainties are given in terms of linear matrix inequalities (LMIs). Furthermore, a convex optimization problem with LMI constraints is formulated to design the output feedback controller which minimizes an upper bound on the worst-case H2 norm for a range of admissible plant perturbations. The technique is illustrated with applications to the design of stabilizer for a single-machine infinite-bus (SMIB) power system. The LMI based control ensures adequate damping for widely varying system operating.

Robust Electric Power System Controllers Synthesized on the Basis of Linear Matrix Inequalities

2018 ◽  
Vol 10 (10) ◽  
pp. 4-19
Author(s):  
Magomed G. GADZHIYEV ◽  
◽  
Misrikhan Sh. MISRIKHANOV ◽  
Vladimir N. RYABCHENKO ◽  
◽  
...  
Keyword(s):  
Power System ◽  
Electric Power ◽  
Linear Matrix Inequalities ◽  
Electric Power System ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Power System Controllers

ON THE SOLVABILITY OF A MIXED PROBLEM WITH DEGREE LAPLACE OPERATORS WITH NONLOCAL BOUNDARY CONDITIONS

2020 ◽  
pp. 85-104
Author(s):  
Shakirbai G. Kasimov ◽  
◽  
Mahkambek M. Babaev ◽  
◽  
Keyword(s):  
Boundary Conditions ◽  
Spectral Problem ◽  
Nonlocal Boundary ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlocal Boundary Conditions ◽  
Laplace Operators ◽  
Initial Boundary Problem ◽  
Initial Boundary Value ◽  
Delayed Time

The paper studies a problem with initial functions and boundary conditions for partial differential partial equations of fractional order in partial derivatives with a delayed time argument, with degree Laplace operators with spatial variables and nonlocal boundary conditions in Sobolev classes. The solution of the initial boundary-value problem is constructed as the series’ sum in the eigenfunction system of the multidimensional spectral problem. The eigenvalues are found for the spectral problem and the corresponding system of eigenfunctions is constructed. It is shown that the system of eigenfunctions is complete and forms a Riesz basis in the Sobolev subspace. Based on the completeness of the eigenfunctions system the uniqueness theorem for solving the problem is proved. In the Sobolev subspaces the existence of a regular solution to the stated initial-boundary problem is proved.

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