Note: This content is accessible to all versions of every browser. However, this browser does not seem to support current Web standards, preventing the display of our site's design details.


Simplified frequency transformation for linear discrete-time, time varying systems with applications to feedback stability analysis

Frequency analysis, including stability margin measures, is a well-known tool for linear time-invariant systems analysis and synthesis. Unfortunately, classical frequency methods cannot be used for systems for which a frequency diagram is not adequately defined, i.e. for linear time varying systems. The presentation begins with definitions and numerical algorithms for frequency diagrams (magnitude, phase) approximation for time varying systems. The main method is based on Singular Value Decomposition (SVD), Discrete Fourier Transform (DFT) and power spectral density (PSD) properties. The second part of the talk concerns a novel method for feedback stability evaluation for linear time-varying, discrete-time control systems. It is assumed that the time-varying system can be described by general discrete-time, time-varying state space model and by equivalent linear input-output (transfer) operator. The proposed method extends not only classical Nyquist feedback stability criterion for time-invariant systems, but also further results proposed by e.g. by Popov for Lurie systems. The proposed method is applicable for linear time-varying, discrete-time systems given in general state-space form. The main tools used are Bode diagrams approximated for time-varying systems, using properties of power spectral density, discrete Fourier transform and Singular Value Decomposition of the system operator. Theoretical considerations are complemented by numerical examples.

Type of Seminar:
Public Seminar
Dr Przemyslaw Orlowski
Institute of Control Engineering, Szczecin University of Technology
Dec 16, 2008   11:00/

ETH Zentrum, Building ETZ, Room E 81
Contact Person:

Prof. Manfred Morari
File Download:

Request a copy of this publication.
Biographical Sketch:
Przemyslaw Orlowski is an Adjunct Professor in the Technical University of Szczecin, Institute of Control Engineering. He received M.Sc. degrees in Electronics and Telecommunication (1999) and Electrical Engineering (1999) both from the Technical University of Szczecin. After 3 years he received Ph.D. (2002) degree in Control. During that time he became interested in discrete-time, time-varying systems also the applications for nonlinear systems.