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.

Transmission Rate by User Antenna Selection for Block Diagonalization Based Multiuser MIMO System

2014 ◽  
Vol E97.B (10) ◽  
pp. 2118-2126 ◽  
Author(s):  
Kentaro NISHIMORI ◽  
Takefumi HIRAGURI ◽  
Hideo MAKINO
Keyword(s):  
Transmission Rate ◽  
Antenna Selection ◽  
Mimo System ◽  
Block Diagonalization ◽  
Multiuser Mimo ◽  
Selection For

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

scholarly journals Robust Position Control of a Two-Sided 1-DoF Impacting Mechanical Oscillator Subject to an External Persistent Disturbance by Means of a State-Feedback Controller

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Firas Turki ◽  
Hassène Gritli ◽  
Safya Belghith
Keyword(s):  
State Feedback ◽  
Position Control ◽  
External Disturbance ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Mechanical Oscillator ◽  
Impact Oscillator ◽  
State Feedback Controller ◽  
The Impact

This paper proposes a state-feedback controller using the linear matrix inequality (LMI) approach for the robust position control of a 1-DoF, periodically forced, impact mechanical oscillator subject to asymmetric two-sided rigid end-stops. The periodic forcing input is considered as a persistent external disturbance. The motion of the impacting oscillator is modeled by an impulsive hybrid dynamics. Thus, the control problem of the impact oscillator is recast as a problem of the robust control of such disturbed impulsive hybrid system. To synthesize stability conditions, we introduce the S-procedure and the Finsler lemmas by only considering the region within which the state evolves. We show that the stability conditions are first expressed in terms of bilinear matrix inequalities (BMIs). Using some technical lemmas, we convert these BMIs into LMIs. Finally, some numerical results and simulations are given. We show the effectiveness of the designed state-feedback controller in the robust stabilization of the position of the impact mechanical oscillator under the disturbance.

Sign in / Sign up

Export Citation Format

Share Document