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Denominator Assignment, Invariants, and Canonical Forms Under Dynamic Feedback Compensation in Linear Multivariable Nonsquare Systems | IEEE Journals & Magazine | IEEE Xplore

Denominator Assignment, Invariants, and Canonical Forms Under Dynamic Feedback Compensation in Linear Multivariable Nonsquare Systems


Abstract:

In this article, we generalize previously reported results for linear, time-invariant, stabilizable multivariable systems described by a strictly proper transfer function...Show More

Abstract:

In this article, we generalize previously reported results for linear, time-invariant, stabilizable multivariable systems described by a strictly proper transfer function matrix P(s) with number of outputs greater than or equal to the number of inputs. By making use of a special kind of a left generalized inverse P(s)_{\alpha }^{\oplus } of P(s), we define and examine the equivalent relation \mathcal {R} relating P(s) with the members of the equivalence class [P(s)]_{R} of the closed loop-transfer function matrices P_{C}(s) obtainable from P(s) by the use of a proper compensator C(s) in the feedback path. For \mathcal {R}, we establish a set of complete invariants and a canonical form. These results give rise to a simple algorithmic procedure for the computation of proper internally stabilizing and denominator assigning compensators C(s) for the class of plants with p=m and having no zeros in the closed right half complex plane: \mathbb {C}^{+} and in the case when p>m plants characterized by right polynomial matrix fraction descriptions with a polynomial matrix numerator having at least one subset of m rows that give rise to a nonsingular polynomial matrix with no zeros in \mathbb {C}^{+}.
Published in: IEEE Transactions on Automatic Control ( Volume: 66, Issue: 10, October 2021)
Page(s): 4903 - 4909
Date of Publication: 11 December 2020

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