MULTIVARIABLE CIRCLE CRITERIA - AN APPROACH BASED ON SECTOR CONDITIONS
The present paper uses appropriate forms of sector conditions in conjunction with the decomposition of a linear operator into two linear operators PHI and G minus PHI , where PHI has a normal transfer function matrix; and proposes a useful stability criterion for a class of multivariable non-linear...
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| Fformat: | Journal article |
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1982
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| Crynodeb: | The present paper uses appropriate forms of sector conditions in conjunction with the decomposition of a linear operator into two linear operators PHI and G minus PHI , where PHI has a normal transfer function matrix; and proposes a useful stability criterion for a class of multivariable non-linear feedback systems. The relevant stability result is developed further by a suitable interpretation of sector conditions in the frequency domain. A particular choice for PHI leads to a generalization of the circle criterion in which the Nyquist plot of the frequency response of scalar systems is replaced by bands swept by circles, whose centers and radii are related in a direct manner to the numerical range of G(j omega ). The result has a simple graphical interpretation and lends itself to a computer implementation which can be shown to be numerically stable. |
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