Title :
Limit-cycle predictions in sampled data systems
Author :
Cameron, R. ; Kouvaritakis, B.
Author_Institution :
University of Bradford, Postgraduate School of Control Engineering, Bradford, UK
fDate :
9/1/1981 12:00:00 AM
Abstract :
For sampled data systems, it is possible to express discrete time convolution in terms of appropriate matrix multiplication. A limiting process then yields the steady-state response to a periodic input. The matrix involved in this operation is a circulant matrix based on the impulse response of the system. Circulant matrices are known to have useful structural properties and permit the association of the frequency domain with the time domain. The use of circulants in the analysis of nonlinear systems provides the means for converting the unwieldy nonlinear equations of continuous systems to simple matrix multiplications. It is then possible to apply numerical range techniques and rederive the circle criterion. The direct application of this approach yields a criterion which is less conservative than that obtained by the simple application of the small-gains theorem. Use of the approach in conjunction with a loop transformation, on the other hand, provides an alternative derivation of the circle criterion for discrete systems. The method can be extended to multivariable systems, and, because of its association with the time domain, it permits the assessment of system stability in the face of imperfect system descriptions, namely truncated impulse responses.
Keywords :
limit cycles; matrix algebra; nonlinear systems; sampled data systems; stability criteria; circle criterion; circulant matrix; continuous systems; discrete systems; discrete time convolution; frequency domain; impulse response; limit cycle predictions; limiting process; loop transformation; matrix multiplication; multivariable systems; nonlinear systems; numerical range techniques; periodic input; sampled data systems; stability; steady-state response; time domain;
Journal_Title :
Control Theory and Applications, IEE Proceedings D
DOI :
10.1049/ip-d.1981.0047