On the robust stability of plant families with poles crossing the imaginary axis: A new small gain condition

2005 ◽  
Author(s):  
Yongdong Zhao ◽  
S. Jayasuriya
Keyword(s):  
Robust Stability ◽  
Imaginary Axis ◽  
Small Gain ◽  
Plant Families

Robust Stability of Closed-Loop Systems Resulting From Nonsequential MIMO-QFT Design

1996 ◽  
Vol 118 (4) ◽  
pp. 753-756 ◽  
Author(s):  
Yongdong Zhao ◽  
Suhada Jayasuriya
Keyword(s):  
Robust Stability ◽  
Imaginary Axis ◽  
Closed Loop ◽  
Extra Condition ◽  
Plant Family ◽  
Small Gain Theorem ◽  
Closed Loop Systems ◽  
Entire Plant ◽  
Small Gain ◽  
Plant Families

Considered in this paper is the question of whether a compensator realized by the MIMO-QFT nonsequential method robustly stabilizes the entire plant family. In order to establish our results, first the classic small gain theorem for robust stability is modified to allow uncertain plant families with poles arbitrarily crossing the imaginary axis, or equivalently, plants in which the number of unstable poles does not remain fixed over all uncertainties. The conventional assumption that the number of unstable poles remain fixed over all uncertainties can be quite restrictive, especially, in the case of plants with structured uncertainties. It is shown that to assure robust stability of the closed loop, resulting from the MIMO-QFT nonsequential approach, one more requirement must be added to the procedure. The needed extra condition can be quite naturally incorporated during the execution of the nonsequential technique. As a result, the proposed condition does not significantly alter the basic MIMO-QFT nonsequential procedure.

scholarly journals Stability Problem of Wave Variable Based Bilateral Control: Influence of the Force Source Design

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Dapeng Tian ◽  
Bao Zhang ◽  
Honghai Shen ◽  
Jiaquan Li
Keyword(s):  
Control System ◽  
Stability Analysis ◽  
Time Delay ◽  
Robust Stability ◽  
Scattering Theory ◽  
Stability Problem ◽  
Bilateral Control ◽  
Wave Variable ◽  
Small Gain ◽  
The Stability

The wave variable has been proposed to achieve robust stability against the time delay in bilateral control system. However, the influence of the force source on the overall system is still not clear. This paper analyzes this problem and proposes a supplement to the stability analysis for wave variable based bilateral control. Based on the scattering theory, it is pointed out that the design of force source decides the passivity of the two-port network of slave robot. This passivity influences the stability of overall system. Based on the characteristic equation and small gain theorem, it is clear that inappropriate designed force source in encoding the wave variable destroys the stability in the presence of time delay. A wave domain filter makes up for the broken stability. The principle of this reparation is explained in this paper. A reference is also provided by the analysis to design the parameter of the wave domain filter. Experiments prove the correctness and validity.

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