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Global stability of nonlinear feedback systems with fractional positive linear parts

Kaczorek Tadeusz

International Journal of Applied Mathematics and Computer Science

2020

Vol. 30, no. 3

493--499

The global (absolute) stability of nonlinear systems with fractional positive and not necessarily asymptotically stable linear parts and feedbacks is addressed. The characteristics u = f(e) of the nonlinear parts satisfy the condition k1e ≤ f(e) ≤ k2e for some positive k1 and k2. It is shown that the fractional nonlinear systems are globally asymptotically stable if the Nyquist plots of the fractional positive linear parts are located on the right-hand side of the circles (−1/k1,−1/k2).

Global stability of nonlinear feedback systemswith positive descriptor linear parts

Kaczorek T.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2019

Vol. 67, nr 1

45--51

The global (absolute) stability of nonlinear systems with negative feedbacks and positive descriptor linear parts is addressed. Transfer matrices of positive descriptor linear systems are analyzed. The characteristics u = f (e) of the nonlinear parts satisfy the condition k1e ≤ f (e) ≤ k2e for some positive k1, k2. It is shown that the nonlinear feedback systems are globally asymptotically stable if the Nyquist plots of the positive descriptor linear parts are located in the right-hand side of the circles (– 1/k1, – 1/k2).

A pilot study on the effect of music-heart beat feedback system on human heart activity

Nomura S., Yoshimura K., Kurosawa Y.

Journal of Medical Informatics & Technologies

2013

Vol. 22

251--256

We developed a music-heart beat feedback system to test the efficacy of the entrainment between music and human heart beat. As a result of regulating the music tempo as 10% faster (namely FAST condition) or slower (SLOW) than heart beat in a real time series, the subjects’ heart rate was successfully modulated as significantly higher in the FAST condition and lower in the SLOW condition. The timeliness regulation of this feedback system may play a key role to bring forth the music-heart beat entrainment.

On reducing the order ot the stabilizing compensator for a linear multivariable plant

Ładziński R.

Archives of Control Sciences

1998

Vol. 7, no. 1/2

69-98

The text covers an in-depth study on the order of the compensator applied in a feedback system for stabilization of the linear, time-invariant, n-th order, multivariable plant. It is shown that all such compensators evolve from the n-th order structure depicted in two forms in Fig. 2 (dotted lines). Presentation includes the so-called reduced and subreduced order compensators and the case of a static output feedback, i.e. the compensator of order zero. All theoretical considerations are supported by examples, in which various types of compensators are synthesized.