Wieslaw Krajewski

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A set of necessary conditions that must be satisfied by the L2 optimal rational transfer matrix approximating a given higher-order transfer matrix, is briefly described. On its basis, an efficient iterative numerical algorithm has been obtained and implemented using standard MATLAB functions. The purpose of this contribution is to make the related computer(More)
The algorithm for ̧ 2 -optimal model reduction described in Krajewski et al. (1995), though computationally efficient, may sometimes fail to converge. In this note, it is shown that, by exploiting the bounds on the eigenvalues of the Jacobian of the associated transition function, a variant can be developed whose convergence to the minima of the considered(More)
The paper deals with the problem of approximating a stable continuous-time multivariable system by minimizing the L 2-norm of a weighted equation error. Necessary and sufficient conditions of optimality are derived, and the main properties of the optimal reduced-order models are presented. Based on these conditions and properties, two efficient procedures(More)
This paper is concerned with the construction of reduced–order models for high–order linear systems in such a way that the L2 norm of the impulse–response error is minimized. Two convergent algorithms that draw on previous procedures presented by the same authors, are suggested: one refers to s–domain representations, the other to time–domain state–space(More)
This paper presents an easily implementable method for determining the set of PID controllers that stabilize an LTI system with or without a time delay while satisfying certain robustness requirements. The adopted approach, which does not require approximating the time delay or solving complex non-algebraic equations, draws directly on the graphic approach(More)
The paper deals with the problem of reducing the order of an original high-order asymptotically stable linear switching system by independently approximating the (stable) LTI systems corresponding to every fixed value of the switching signal. Precisely, each reduced-order model is obtained by minimising the L<inf>2</inf> norm of a weighted equation error by(More)