Open AccessSwitching regulation based stabilisation of discrete‐time 2D switched systems with stable and unstable modes
Author(s) -
Hua Changchun,
Liu Guopin,
Guan Xinping
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.2017.1052
Subject(s) - control theory (sociology) , discrete time and continuous time , exponential stability , asynchronous communication , state (computer science) , controller (irrigation) , stability (learning theory) , linear matrix inequality , mathematics , computer science , control (management) , nonlinear system , mathematical optimization , physics , algorithm , computer network , statistics , quantum mechanics , artificial intelligence , machine learning , agronomy , biology
This study investigates the stabilisation problem for a class of discrete‐time two‐dimensional (2D) switched systems. Here the 2D systems mean that the state evolves following two independent directions, which are usually represented as horizontal states and vertical states. The considered systems are represented by Roesser model and incorporate both stable and unstable modes. Based on a switching signal regulation approach, which restricted the switching number as well as the running time ratio between the unstable and stable modes, the exponential stability condition is established for the 2D switched systems with synchronous switching. Besides, solving the proposed stabilisation results in linear matrix inequality form, the stabilising controller gains can be obtained. Moreover, considering the time delay in the controllers when the switching occurs, the proposed results are extended to the stabilisation problem for the 2D switched systems under asynchronous switching. A numerical example further demonstrates the validity of the developed results.