A cutting plane method for solving KYP-SDPs
Automatica (Journal of IFAC)
On the Kalman---Yakubovich---Popov lemma and the multidimensional models
Multidimensional Systems and Signal Processing
Numerical experiments with universal barrier functions for cones of Chebyshev systems
Computational Optimization and Applications
Brief paper: An alternative Kalman-Yakubovich-Popov lemma and some extensions
Automatica (Journal of IFAC)
Optimization of the higher density discrete wavelet transform and of its dual tree
IEEE Transactions on Signal Processing
Interior-Point Method for Nuclear Norm Approximation with Application to System Identification
SIAM Journal on Matrix Analysis and Applications
Brief Positive polynomial matrices and improved LMI robustness conditions
Automatica (Journal of IFAC)
A convex optimization method to solve a filter design problem
Journal of Computational and Applied Mathematics
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The Nesterov characterizations of positive pseudopolynomials on the real line, the imaginary axis, and the unit circle are extended to the matrix case. With the help of these characterizations, a class of optimization problems over the space of positive pseudopolynomial matrices is considered. These problems can be solved in an efficient manner due to the inherent block Toeplitz or block Hankel structure induced by the characterization in question. The efficient implementation of the resulting algorithms is discussed in detail. In particular, the real line setting of the problem leads naturally to ill-conditioned numerical systems. However, adopting a Chebyshev basis instead of the natural basis for describing the polynomial matrix space yields a restatement of the problem and of its solution approach with much better numerical properties.