Coprime sampling for system stabilization with FIR multirate controllers

Coprime sampling has in the past found applications in fractional sampling rate alteration, spatial array processing, radar signal processing, system identification, and fractionally spaced channel-equalization. This paper revisits multirate feedback control systems in the context of coprime sampling theory. It is shown in particular that the system from the primary input to the output node can be stabilized with an FIR controller when the feedback rate is higher than the input and output rates. On the other hand, the system from the primary input to the feedback signal node can be stabilized with an FIR controller, whether the feedback rate is higher or lower than the input and output rates. These results hold under a coprimality assumption on certain transfer matrices which arise in the plant description. The assumption is mild in the sense that it is almost always satisfied in practice.

[1]  P. P. Vaidyanathan,et al.  MIMO biorthogonal partners and applications , 2002, IEEE Trans. Signal Process..

[2]  Soura Dasgupta.  An approach to multirate control , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[3]  P. P. Vaidyanathan,et al.  System Identification With Sparse Coprime Sensing , 2010, IEEE Signal Processing Letters.

[4]  Inbar Fijalkow,et al.  Fractionally spaced equalizers , 1996, IEEE Signal Process. Mag..

[5]  P. P. Vaidyanathan,et al.  Sparse Sensing With Co-Prime Samplers and Arrays , 2011, IEEE Transactions on Signal Processing.

[6]  G. Kranc,et al.  Input-output analysis of multirate feedback systems , 1957 .

[7]  P. P. Vaidyanathan,et al.  Signal Processing and Optimization for Transceiver Systems , 2010 .

[8]  F. R. Gantmakher.  The Theory of Matrices , 1984 .

[9]  K. Poolla,et al.  Robust control of linear time-invariant plants using periodic compensation , 1985 .

[10]  Li Qiu,et al.  H∞ design of general multirate sampled-data control systems , 1994, Autom..

[11]  Alan V. Oppenheim,et al.  Discrete-time Signal Processing. Vol.2 , 2001 .

[12]  Peter Lancaster,et al.  The theory of matrices , 1969 .

[13]  P. Vaidyanathan.  Multirate Systems And Filter Banks , 1992 .

[14]  John R. Treichler,et al.  Fractionally spaced equalizers. How long should they really be , 1996 .

[15]  B. Francis,et al.  Stability Theory for Linear Time-Invariant Plants with Periodic Digital Controllers , 1988 .

[16]  Benjamin C. Kuo,et al.  AUTOMATIC CONTROL SYSTEMS , 1962, Universum:Technical sciences.

[17]  P. Vaidyanathan,et al.  Coprime sampling and the music algorithm , 2011, 2011 Digital Signal Processing and Signal Processing Education Meeting (DSP/SPE).

[18]  P. P. Vaidyanathan,et al.  Theory of Sparse Coprime Sensing in Multiple Dimensions , 2011, IEEE Transactions on Signal Processing.

[19]  Thomas Kailath,et al.  Linear Systems , 1980 .