Title :
Distributed stabilisation of spatially invariant systems via positive polynomial approach: MIMO systems case
Author_Institution :
Inst. of Inf. Theor. & Autom., Prague, Czech Republic
Abstract :
The linear spatially-distributed time-invariant systems with multiple inputs and multiple outputs, modelled by the bivariate transfer function are considered. Stabilisation technique is based on the relationship between stability of the closed-loop bivariate polynomial and positiveness of a related polynomial matrix on the unit circle. Since such matrix is not linear in coefficients of the original polynomial and cannot be used for controller design directly, a linearising factorisation is found. 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.
Keywords :
MIMO systems; closed loop systems; distributed control; matrix algebra; polynomials; stability; transfer functions; MIMO systems case; bivariate transfer function; closed-loop bivariate polynomial; controller design; distributed stabilisation; heat conduction; linear spatially distributed time-invariant systems; linearising factorisation; long thin metal rod; multiple inputs and multiple outputs; polynomial matrix; positive polynomial approach; spatially invariant systems; stabilisation technique; temperature heaters; temperature sensors; unit circle; Heating; Polynomials; Stability criteria; Symmetric matrices; Thermal stability; Transfer functions; Spatially-invariant systems; multiple-inputs-multiple-outputs systems; polynomial methods; positive polynomials;
Conference_Titel :
Carpathian Control Conference (ICCC), 2012 13th International
Conference_Location :
High Tatras
Print_ISBN :
978-1-4577-1867-0
DOI :
10.1109/CarpathianCC.2012.6228607