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Pozycja Open Access An introduction to SVD-DFT frequency analysis for time-varying systems(Wydawnictwo Uczelniane Politechniki Szczecińskiej, 2003) Orłowski, Przemysław; Technical University of SzczecinThe paper develops tools and methods for linear time-varying, discrete-time sys-tems analysis. It consists of theoretical background, definitions and numerical algorithms for frequency characteristics approximation. The main method is based on Singular Value Decomposition SVD, Discrete Fourier Transform DFT and power density spectrum proper-ties. A few illustrative numerical examples are included. Three different models have been analysed: oscillatory element, low pass filter and variable structure system. For better evaluation, results for presented method are compared with classical Bode characteristics.Pozycja Open Access Output uncertainty estimates for a class of non-linear discrete-time systems(Wydawnictwo Uczelniane Politechniki Szczecińskiej, 2004) Orłowski, Przemysław; Technical University of Szczecin, Control Engineering InstituteThe paper develops a mathematical framework which helps to analyse a class of non-linear, uncertain, discrete-time systems defined on finite horizon control. Uncertainty in the system is modelled by unknown (norm bounded) additive perturbations of the system matrices. The main purpose of the paper is to derive estimates for output deviations system from the output of the nominal (unperturbed) one. These estimates use norms of certain dynamical operators defined on a finite time interval.Pozycja Open Access Periodic Linear Time-Varying System Norm Estimation Using Running Finite Time Horizon Transfer Operators(Department of Engineering, University of Ferrara, Ferrara, Italy, 2010-11) Orlowski, Przemyslaw; West Pomeranian University of Technology, Szczecin, Department of Control and MeasurementsA novel method for norm estimation for dynamical linear time-varying systems is developed. The method involves operators description of the system model i.e. transfer operator. The transfer operator defined for finite time horizon can be described by finite dimensional matrix whereas for infinite time horizon the operator is infinite dimensional. The norm estimate for infinite time horizon is based on analysis of a running series of the finite time horizon norm properties.Pozycja Open Access Properties of the frequency SVD-DFT for discrete LTV systems based on first order examples(2006) Orlowski, Przemyslaw; Technical University of SzczecinThe paper develops frequency analysis tools for linear time-varying (LTV), discrete-time systems. The main method is based on the properties of the Singular Value De-composition (SVD), Discrete Fourier Transform (DFT) and Power Spectral Density (PSD). The analysis is carried out for a system with first order dynamics. The general objective of this paper is to examine how system frequency diagrams are depend on the variability of particular parameters. Especially, it is examined how the variability of three matrices of the state space model (scalars, in the 1st order case) influence the approximated Bode diagrams. A few cases of the variability of each matrix, in particular with different frequencies and phase shifting, are considered. Moreover, the analysis is carried out for different cases of the system parameters. The results of analysis for each case are shown in four diagrams: amplitude, phase, impulse and step responses. On the basis of these examples the most important features in each example are characterized.Pozycja Open Access Robust control design for a class of non-linear systems(2003) Orłowski, Przemysław; Technical University of SzczecinThe paper develops design methods for a class of uncertain, non-linear control systems. It extends the robustness analysis techniques of linear time varying systems and in particular the associated computational methodology to a class of nonlinear systems. It can be divided into following four parts: theoretical background, identification procedure, structure of feedback control system and cost functional for control optimisation for uncertain non-linear systems, control optimisation algorithm and the method for estimate the worst case output uncertainty norm of the system.Pozycja Open Access Selected Problems of Uncertainty Estimates for Non-linear Discrete-Time Systems(2000) Orłowski, Przemysław; Technical University of SzczecinThe paper develops a mathematical framework which helps to analyse the following class of finite horizon control problems for uncertain nonlinear discrete-time systems. [ WZORY] Uncertainty in the system description are modelled by unknown (norm bounded) mixed additive-multiplicative perturbations of the system matrix. It is assumed that the nominal control has feedback form. If the nominal control will be applied to the uncertain system the state and output will be (in general) different. Formulas for deriving estimates for the deviations of the output of perturbed system from the output of the nominal one has been presented. These estimates use norms of certain dynamical operators defined on a finite time interval.