Performance and robustness preservation in MIMO systems when applying SPR Substitutions

• Published in: International journal of systems science Vol. 39; no. 12; pp. 1153 - 1163
• Main Authors: Fernández-Anaya, G., Martínez-García, J.C., Kučera, V., Aguilar-George, D.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Group 01.12.2008; Taylor & Francis
• Subjects: Applied sciences; Computer science; control theory; systems; Control system synthesis; Control theory. Systems; controller optimality; Exact sciences and technology; linear time-invariant systems; parameterization of stabilizing controllers; robust control; substitution of the complex Laplace variable; Well-posedness; MIMO system; Transfer matrix; Suboptimal control; Invariant subspace; linear time-invariant systems; H infinite control; Coprime factorization; Feedback regulation; Continuous time; Tracking task; H∞-controller optimality; Parameterization; Positive system; Complex variable method; Closed feedback; Robust control; Linear time invariant system; Uncertain system; substitution of the complex Laplace variable; Robustness; parameterization of stabilizing controllers; Motion control; Well-posedness
• ISSN: 0020-7721; 1464-5319
• DOI: 10.1080/00207720802088124

We are concerned in this article with controlled linear time-invariant multi input multi output systems in continuous-time. We study here the preservation under strict positive real substitutions (of zero relative degree) of coprime factorisations as well as stabilising properties in parametrised controllers. We also tackle here both the preservation of well-posedness (of the tracking feedback control scheme) and the preservation of H ∞ -optimality properties in some classes of closed-loop systems affected by multiplicative unstructured uncertainty, including the so-called suboptimal H ∞ -control problem by stable controllers (i.e. preservation of both strong stabilisation and H ∞ -boundedness). †A preliminary version of this article has been first presented at MTNS'2004, Lovaine la Neuve, Belgium, 2004.