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

• 成果类型: Article
• 署名作者: Vardulakis, Antonis; Yannakoudakis, Aristotelis; Wei, Cui; Chai, Tianyou
• 署名单位: Aristotle University of Thessaloniki; Northeastern University - China
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3044009
• 发表日期: 2021
• 页码: 4903-4909
• 关键词: Denominator assignment; invariant under dynamic output feedback; nonsquare transfer function matrix; proper stabilizing controllers

摘要

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)(circle plus) a of P(s), we define and examine the equivalent relation 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 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: 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 C+.