A multivariable feedback system y(s)=G(s)x(s), x(s) = u(s)- F(s)y(s) is treated where G(s) ≜ (g kl (s)) is the transfer function matrix of a plant and F(s) ≜ diag(f 1 (s),...,fn(s)) is that of a controller. A new bound for the transfer function h j (s) that relates y j (s) to u j (s) when f j (s)≡ 0 is given. The main result reads |h j (s)- g jj (s)| k (s)-1+ g kk (s)| > a k (s) for k = 1,... ,n; k≠j. Here, A ≜ diag(a 1 (s),...,a n (s)) is a diagonal matrix which makes A-B a semi-M-matrix where B ≜ (b kl ) is given by b kk =0, b kl = |g kl (s)| (k≠l). A similar result is also obtained for the inverse transfer function.

Bounds for closed-loop transfer functions of multivariable systems

This survey paper presents a comprehensive review of work in the field of non-linear oscillations. A brief discussion of second-order systems is followed by a presentation of exact criteria, approximate analytical methods and computational techniques for limit cycles in single variable systems. Multivariate systems are then covered from an analogous viewpoint which allows the reader to clearly identify both how single variable methods have been extended and the possibilities for further research. Particular emphasis is placed on describing function methods since it is believed that, where exact solutions are not possible, the approach may not only give approximate solutions but provides good insight for further computational or simulation studies. The coverage is essentially restricted to continuous lumped parameter systems and includes both free and forced oscillations. Several applications of the theories in various fields of engineering and science are discussed and indicate the broad interest in non-l...

A survey on non-linear oscillations

Acknowledgements Notation vii Chapter 1 General Introduction and Literature Review 1.

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P.A. Cook

Papers

Nyquist-Plot Methods Of Investigating Multivariable Feedback Systems