Yves Genin

On Sigma-lossless transfer functions and related questions

Abstract This paper is concerned with a systematic approach to the properties of ∑-lossless rational transfer functions in the discrete as well as in the continuous time case. As a result, a unifying framework is revealed where several known results fit naturally. Special attention is given to the embedding problem of the Lyapunov equation in view of its direct application to generalized Levinson algorithms.

Optimization Problems over Positive Pseudopolynomial Matrices

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.

Positivity and Linear Matrix Inequalities

In this paper we first recall the general theory of Popov realizations of parahermitian transfer functions in the context of generalized state space systems. We then use this general framework to derive linear matrix inequalities for some particular applications in systems and control. Finally, we indicate how these problems can be solved numerically and what specific numerical difficulties can be encountered in these applications.

Real and complex stability radii of polynomial matrices

Analytic expressions are derived for the complex and real stability radii of non-monic polynomial matrices with respect to an arbitrary stability region of the complex plane. Numerical issues for computing these radii for different perturbation structures are also considered with application to robust stability of Hurwitz and Schur polynomial matrices

Discarding data may help in system identification

We present results concerning the parameter estimates obtained by prediction error methods in the case of input that are insufficiently rich. Such input signals are typical of industrial measurements where occasional stepwise reference changes occur. As is intuitively obvious, the data located around the input signal discontinuities carry most of the useful information. Using singular value decomposition (SVD) techniques, we show that in noise undermodeling situations, the remaining data may introduce large bias on the model parameters with a possible increase of their total mean square error. A data selection criterion is then proposed to discard such poorly informative data to increase the accuracy of the transfer function estimate. The system discussed in particular is a SISO ARMAX system.

Stability radii of polynomial matrices

We derive analytic expressions for the stability radius of polynomial matrices for all Holder norms and discuss numerical issues for computing these stability radii for the 1, 2 and /spl infin/ norm.

Discarding data to perform more accurate system identification

Presents results concerning the parameter estimates obtained by prediction error methods in the case of system input signals that are insufficiently rich. Such input signals are typical of industrial measurements where occasional stepwise reference changes occur. Using singular value decomposition techniques, the authors propose a new data selection criterion that discards the poorly informative data in order to decrease the total mean square error (MSE) of the estimated parameters.

Stability radius and optimal scaling of discrete-time periodic systems

Abstract Robust stability properties of periodic discrete time systems are investigated. Analytic expressions are derived for the stability radius in the scalar case.