On stabilisability of 2-D MIMO shift-invariant systems

0398772 - ÚTIA 2014 RIV GB eng J - Journal Article
Augusta, Petr - Augustová, Petra
On stabilisability of 2-D MIMO shift-invariant systems.
Journal of the Franklin Institute-Engineering and Applied Mathematics. Roč. 350, č. 10 (2013), s. 2949-2966. ISSN 0016-0032. E-ISSN 1879-2693
R&D Projects: GA ČR GPP103/12/P494
Institutional support: RVO:67985556
Keywords : spatially invariant system * stabilisation * multiple-input-multiple-output system, * positive polynomial
Subject RIV: BC - Control Systems Theory
Impact factor: 2.260, year: 2013
http://library.utia.cas.cz/separaty/2013/TR/augusta-0398772.pdf

We concentrate on the linear spatially distributed time-invariant two-dimensional systems with multiple inputs and multiple outputs and with control action based on an array of sensors and actuators connected to the system. The system is described by the bivariate matrix polynomial fraction. Stabilisation of such systems is based on the relationship between stability of a bivariate polynomial and positiveness of a related polynomial matrix on the unit circle. Such matrices are not linear in the controller parameters, however, in simple cases, a linearising factorisation exists. It allows to describe the control design in the form of a linear matrix inequality. In more complicated cases, linear sufficient conditions are given. This concept is applied to a system with multiple outputs—a heat conduction in a long thin metal rod equipped with an array of temperature sensors and heaters, where heaters are placed in larger distances than sensors.
Permanent Link: http://hdl.handle.net/11104/0226296