International audienceThis correspondence investigates the choice of a free parameter, usually related to time scale, that minimizes the error energy when approximating a given signal with some widely used orthonormal basis functions. The proposed solution is the hest that can be achieved with the limited required knowledge of the signal. It is appealing for experimental data for which no exact mathematical expression is available

Abstract-A new online method to optimize the free parameter in adaptive Laguerre-based filters is presented. It is based on the minimization of a criterion that is equivalent to an upper bound for the quadratic approximation error. The proposed technique presents a fast convergence and a good robustness.

We present an efficient model reduction procedure based on the Laguerre description of the system to be approximated. Using a one-order operator defined in the Laplace domain we construct a pencil of functions and formulate the problem as the minimization of the L 2 ̟ R + criterion. The use of a weight function in the inner product definition allows a control of the time-error spreading in model reduction procedure. We show how the required Gram matrix can be computed efficiently and prove that the impulse response of the reduced model is also in L 2 ̟ R +. The transfer function approach allows an immediate and promising application in model reduction of infinite dimensional systems. An extension to MIMO systems is also given.

International audienceSome fundamental properties of an impulse response Gramian for linear, time-invariant, asymptotically stable, discrete single-input-single-output (SISO) systems are derived. This Gramian is system invariant and can be found by solving a Lyapunov equation. The connection with standard controllability, observability, and cross Gramians is proven. The significance of these results in model-order reduction is highlighted with an efficient procedure

International audienceKautz functions have received much attention in the recent mathematical modeling and identification literature. These functions which involve free parameters can approximate efficiently signals with strong oscillatory behavior. We consider here the choice of the free parameters in discrete (two-parameter) Kautz approximation. Using a key relationship between Kautz and Laguerre expansions we derive an upper bound for the quadratic truncation error. Minimization of this upper bound yields pertinent parameters, whose computation then requires reduced knowledge of the function to be modeled