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Off-axis multivariable circle stability criterion

Off-axis multivariable circle stability criterion

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In 1968, the scalar circle stability criterion was extended by Cho and Narendra to the off-axis case by the use of multipliers Q, Q−1 which have an RL or RC realise structure, so that the product of the linear portion of the feedback system and the multiplier was positive-real. Fabl, Freedman and Zames produced a multivariable on-axis circle criterion for systems whose linear part is normal for all frequencies. As yet the off-axis circle criterion has not yet been established for the multivariable case, although Cook (1976) has shown that a criterion of this type does provide the conditions for the absence of limit cycles. Utilising the loop transformation theorem and the passivity theorem, an off-axis multivariable circle stability criterion is established via the method of multipliers for nonlinear feedback systems with a normal linear operator. The criterion is shown to have a simple graphical interpretation based on the Nyquist plots of the eigenvalues of the system.

References

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