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The properties of low pas first order LTV filters

Walczak J., Piwowar A.

Poznan University of Technology Academic Journals. Electrical Engineering

2011

No. 66

137--144

In this paper analysis of impulsive response and stability conditions of first order linear parametric filters has been carried out. The parameters of these filters have been described by some non-periodic functions. The affiliation of models of LTV (linear time-varying) filters to class of frozen systems (system with slowly varying coefficients) has been shown. In this article the BIBO (bounded input bounded output) stability of LTV filters for strictly positive parametric function has been proved using the generalized eigenvalue method.

Numerically robust synthesis of discrete-time H[infinity] estimators based on dual J-lossless factorisations

Suchomski P.

Control and Cybernetics

2003

Vol. 32, no 4

761-802

An approach to the numerically reliable synthesis of the H[infinity] suboptimal state estimators for discretised continuous-time processes is presented. The approach is based on suitable dual J-lossless factorisations of chain-scattering representations of estimated processes. It is demonstrated that for a sufficiently small sampling period the standard forward shift operator techniques may become ill-conditioned and numerical robustness of the design procedures can be significantly improved by employing the so-called delta operator models of the process. State-space models of all H[infinity] sub-optimal estimators are obtained by considering the suitable delta-domain algebraic Riccati equation and the corresponding generalised eigenproblem formulation. A relative condition number of this equation is used as a measure of its numerical conditioning. Both regular problems concerning models having no zeros on the boundary of the delta-domain stability region and irregular (non-standard) problems of models with such zeros are examined. For the first case, an approach based on a dual J-lossless factorisation is proposed while in the second case an extended dual J-lossless factorisation based on a zero compensator technique s required. Two numerical examples are given to illustrate some properties of the considered delta-domain approach.