New results on robust stability analysis and synthesis for MIMO uncertain systems

• Published in: IET control theory & applications Vol. 12; no. 10; pp. 1421 - 1430
• Main Authors: Celentano, Laura, Basin, Michael
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 03.07.2018
• Subjects: adaptive control; additional bounded input signals; additional bounded nonlinearities; control signal; control system; control system synthesis; developed methodologies; dynamic matrix; linear systems; majorant system; maximum time; MIMO systems; MIMO uncertain systems; multiinput multioutput system; nonlinear control systems; nonlinearity; rate‐bounded disturbance; rational multiaffine structure; reference signal; Research Article; robust control; robust controller; robust stability analysis; synthesis; theoretical preliminary results; theoretical results; uncertain electro‐mechanical system; uncertain LTI system; uncertain MIMO system; uncertain system; uncertain systems; unmeasurable state; robust controller; uncertain electro-mechanical system; additional bounded nonlinearities; rate-bounded disturbance; developed methodologies; uncertain LTI system; multiinput multioutput system; unmeasurable state; dynamic matrix; maximum time; robust stability analysis; MIMO uncertain systems; robust control; reference signal; control system; synthesis; theoretical preliminary results; uncertain systems; nonlinearity; adaptive control; control system synthesis; uncertain system; linear systems; control signal; MIMO systems; uncertain MIMO system; additional bounded input signals; nonlinear control systems; rational multiaffine structure; theoretical results; majorant system
• ISSN: 1751-8644; 1751-8652; 1751-8652
• DOI: 10.1049/iet-cta.2018.0101

This paper provides theoretical preliminary results and develops a first methodology, that allows one to efficiently estimate the maximum time constant of a dynamic matrix of an uncertain system with rational multi-affine structure with respect to parameters, and a second one to find a majorant system of a multi-input multi-output (MIMO) system with rational multi-affine structure with respect to parameters. The developed methodologies are used to estimate the evolution of an uncertain linear time-invariant (LTI) system with additional bounded nonlinearities and/or additional bounded input signals. Moreover, the above results are also used to design a robust controller for an uncertain MIMO system with unmeasurable states and subject to a rate-bounded disturbance in order to track a rate-bounded reference signal. The obtained theoretical results are illustrated by three examples. The first two examples deal with the analysis of a LTI system with bounded disturbances and measurement noise, and additional bounded and not bounded nonlinearities, respectively; in the second example a new control law with saturation is also designed. In the last example, a robust controller for an uncertain electro-mechanical system with unmeasurable state is designed to track a rate-bounded reference signal in the presence of a disturbance with bounded derivative.