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TECHNICAL PAPERS

# Robust Stability of Sequential Multi-input Multi-output Quantitative Feedback Theory Designs

[+] Author and Article Information
Murray L. Kerr

Department of Mechanical Engineering,  The University of Queensland, Brisbane, QLD 4072, Australiamkerr@tamu.edu

Department of Mechanical Engineering,  Texas A&M University, College Station, TX 77843sjayasuriya@mengr.tamu.edu

Samuel F. Asokanthan

Department of Mechanical and Materials Engineering,  The University of Western Ontario, London, Ontario N6A 5B9, Canadasasokanthan@eng.uwo.ca

For a square, $n×n$ plant TFM, a multivariable pole or zero of the TFM is considered to be pinned (12) to a subset ${i1,…,im}$, $m, of the input (output) direction if its input (output) direction vector as given by the singular value decomposition, possesses non-zero entries for elements ${i1,…,im}$ and zero otherwise.

J. Dyn. Sys., Meas., Control 127(2), 250-256 (May 24, 2004) (7 pages) doi:10.1115/1.1898233 History: Received August 19, 2003; Revised May 24, 2004

## Abstract

This paper re-examines the stability of multi-input multi-output (MIMO) control systems designed using sequential MIMO quantitative feedback theory (QFT). In order to establish the results, recursive design equations for the SISO equivalent plants employed in a sequential MIMO QFT design are established. The equations apply to sequential MIMO QFT designs in both the direct plant domain, which employs the elements of plant in the design, and the inverse plant domain, which employs the elements of the plant inverse in the design. Stability theorems that employ necessary and sufficient conditions for robust closed-loop internal stability are developed for sequential MIMO QFT designs in both domains. The theorems and design equations facilitate less conservative designs and improved design transparency.

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## Figures

Figure 1

MIMO control structure

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