Open AccessNew results on robust stability analysis and synthesis for MIMO uncertain systems
Author(s) -
Celentano Laura,
Basin Michael
Publication year - 2018
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2018.0101
Subject(s) - bounded function , control theory (sociology) , mathematics , affine transformation , linear system , controller (irrigation) , mimo , computer science , control (management) , beamforming , mathematical analysis , statistics , artificial intelligence , pure mathematics , agronomy , biology
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.