Title :
Stability and stabilization of a class of ill-conditioned second order differential linear repetitive processes
Author :
Dabkowski, Pawel ; Galkowski, Krzysztof ; Rogers, Eric
Author_Institution :
Inst. of Phys., Nicolaus Copernicus Univ. in Torun, Torun, Poland
Abstract :
This paper considers differential linear repetitive processes which are a distinct class of 2D systems whose dynamics evolve over a subset of the upper right quadrant of the 2D plane. In particular, information propagation in one direction only occurs over a finite duration and is governed by a matrix differential linear equation. A stability theory exists for these processes but a problem arises in its application to second order processes due to the possible ill-conditioning of the leading coefficient matrix in the state-space model. Here we derive new results on stability analysis and control law design for this case by first transforming the second-order state-space model to an equivalent first-order descriptor system, thus avoiding the necessity of inverting a possibly ill-conditioned matrix. The results developed here can be computed using linear matrix inequalities (LMIs).
Keywords :
control system synthesis; differential algebraic equations; linear matrix inequalities; linear systems; multidimensional systems; stability; state-space methods; 2D system; control law design; differential linear repetitive process; first-order descriptor system; ill-conditioned matrix; information propagation; linear matrix inequalities; matrix differential linear equation; second-order state-space model; stability theory; Asymptotic stability; Control systems; Iterative algorithms; Linear matrix inequalities; Physics; Power system analysis computing; Power system economics; Power system modeling; Robust stability; State feedback;
Conference_Titel :
Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on
Conference_Location :
Shanghai
Print_ISBN :
978-1-4244-3871-6
Electronic_ISBN :
0191-2216
DOI :
10.1109/CDC.2009.5400093