Matrix Stabilization Using Differential Equations

We consider the problem of stabilizing a matrix by a correction of minimal norm: Given a square matrix that has some eigenvalues with positive real part, find the nearest matrix having no eigenvalu...

[1]  Daniel Kressner,et al.  Low rank differential equations for Hamiltonian matrix nearness problems , 2015, Numerische Mathematik.

[2]  Hanna Walach,et al.  Discretized Dynamical Low-Rank Approximation in the Presence of Small Singular Values , 2016, SIAM J. Numer. Anal..

[3]  A. Lewis,et al.  A Nonsmooth, Nonconvex Optimization Approach to Robust Stabilization by Static Output Feedback and Low-Order Controllers , 2003 .

[4]  C. Lubich,et al.  A projector-splitting integrator for dynamical low-rank approximation , 2013, BIT Numerical Mathematics.

[5]  Danny C. Sorensen,et al.  Deflation Techniques for an Implicitly Restarted Arnoldi Iteration , 1996, SIAM J. Matrix Anal. Appl..

[6]  Nicola Guglielmi,et al.  Computing the Structured Pseudospectrum of a Toeplitz Matrix and Its Extreme Points , 2012, SIAM J. Matrix Anal. Appl..

[7]  Joseph F. Grcar,et al.  Operator Coefficient Methods for Linear Equations , 2012, 1203.2390.

[8]  Paul Van Dooren,et al.  Nearest stable system using successive convex approximations , 2013, Autom..

[9]  Michael L. Overton,et al.  Fast Approximation of the HINFINITY Norm via Optimization over Spectral Value Sets , 2013, SIAM J. Matrix Anal. Appl..

[10]  M. Overton,et al.  FAST APPROXIMATION OF THE H∞ NORM VIA OPTIMIZATION OVER SPECTRAL VALUE SETS∗ , 2012 .

[11]  Michael L. Overton,et al.  Fast Algorithms for the Approximation of the Pseudospectral Abscissa and Pseudospectral Radius of a Matrix , 2011, SIAM J. Matrix Anal. Appl..

[12]  L. Trefethen Spectra and pseudospectra , 2005 .

[13]  Christian Lubich,et al.  Dynamical low-rank approximation: applications and numerical experiments , 2008, Math. Comput. Simul..

[14]  Punit Sharma,et al.  On computing the distance to stability for matrices using linear dissipative Hamiltonian systems , 2016, Autom..

[15]  D. K. Frederick,et al.  BENCHMARK PROBLEMS FOR COMPUTER-AIDED CONTROL SYSTEM DESIGN , 1989 .

[16]  Nicola Guglielmi,et al.  Low-Rank Dynamics for Computing Extremal Points of Real Pseudospectra , 2013, SIAM J. Matrix Anal. Appl..

[17]  Tosio Kato Perturbation theory for linear operators , 1966 .