Vector Randomization Methods

In this chapter we address the issue of generating random samples of real and complex vector vectors in l p norm balls, according to the uniform distribution. We present efficient algorithms based upon the theoretical developments of the Chap. 15. The presented methods are non-asymptotic, and therefore, they can be easily implemented on parallel and distributed architectures.

[1]  Giuseppe Carlo Calafiore,et al.  Radial and Uniform Distributions in Vector and Matrix Spaces for Probabilistic Robustness , 1999 .

[2]  J. L. Hock,et al.  An exact recursion for the composite nearest‐neighbor degeneracy for a 2×N lattice space , 1984 .

[3]  James Durbin,et al.  The fitting of time series models , 1960 .

[4]  Mervin E. Muller,et al.  A note on a method for generating points uniformly on n-dimensional spheres , 1959, CACM.

[5]  P. Djurić,et al.  Uniform random parameter generation of stable minimum-phase real ARMA (p,q) processes , 1997, IEEE Signal Processing Letters.

[6]  Fabrizio Dabbene,et al.  On the Generation of Random Stable Polynomials , 2011, Eur. J. Control.

[7]  James S. Meditch,et al.  A canonical parameter space for linear systems design , 1978 .

[8]  Ülo Nurges.  Robust pole assignment via reflection coefficients of polynomials , 2006, Autom..

[9]  Constantino M. Lagoa,et al.  A risk adjusted approach to robust simultaneous fault detection and isolation , 2007, Autom..

[10]  N. Levinson.  The Wiener (Root Mean Square) Error Criterion in Filter Design and Prediction , 1946 .

[11]  M. Sznaier,et al.  An algorithm for sampling subsets of H/sub /spl infin// with applications to risk-adjusted performance analysis and model (in)validation , 2005, IEEE Transactions on Automatic Control.

[12]  R.M. Fujimoto,et al.  Parallel and distributed simulation systems , 2001, Proceeding of the 2001 Winter Simulation Conference (Cat. No.01CH37304).

[13]  Jie Chen,et al.  Probabilistic bounds for l1 uncertainty model validation , 2007, Autom..

[14]  Jie Chen,et al.  Probabilistic Estimates for Mixed Model Validation Problems With ${\cal H}_{\infty}$ Type Uncertainties , 2010, IEEE Transactions on Automatic Control.

[15]  L. Mirsky,et al.  The Theory of Matrices , 1961, The Mathematical Gazette.

[16]  J. S. Hicks,et al.  An efficient method for generating uniformly distributed points on the surface of an n-dimensional sphere , 1959, CACM.

[17]  Li Qiu,et al.  Topics in Control and its Applications , 1999 .

[18]  Ülo Nurges.  Reflection Coefficients of Polynomials and Stable Polytopes , 2009, IEEE Transactions on Automatic Control.