Stability Analysis and Stabilization of Discrete-Time 2D Switched Systems

Stability analysis and stabilization of 2-D switched systems under arbitrary and restricted switchings

“…So far, many important results have been reported in the literature, see for example, Bouagada and Dooren (2013), Gao, Lam, Xu, and Wang (2004), Li and Gao (2012), Paszke, Lam, Gałkowski, Xu, and Lin (2004), Wu, Shi, Gao, and Wang (2008), Wu, Yao, and Zheng (2012), Xiang and Huang (2013), Yang, Xie, and Zhang (2006) and ✩ The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor James Lam under the direction of Editor Ian R. Petersen.…”

“…This class of systems can correspond to 2-D switched systems. Recently, a number of reports on 2-D discrete switched systems appeared, see for example, Benzaouia, Hmamed, Tadeo, and Hajjaji (2011) and Xiang and Huang (2013). The stability analysis was investigated in Benzaouia et al (2011) for discrete-time 2-D switched systems in Roesser model based on common and multiple Lyapunov functions.…”

“…The stability analysis was investigated in Benzaouia et al (2011) for discrete-time 2-D switched systems in Roesser model based on common and multiple Lyapunov functions. The stability analysis and stabilization problems were considered in Xiang and Huang (2013) for 2-D discrete switched systems by a model of Roesser type. Although there are some initial results for 2-D switched systems, it is noted that the aforementioned research efforts have been focused on the Roesser type.…”

New results on saturation overflow stability of 2-D state-space digital filters described by the Fornasini–Marchesini second model

“…The knowledge of 2-D systems is very important to deal with the problems in various areas such as image data processing and transmission [2], process of gas filtration [3], energy exchanging process and electricity transmission, thermal processes in chemical reactors [4], river pollution modeling [5], grid-based wireless sensor networks [6], 2-D digital filtering [7][8][9][10][11][12][13][14], 2-D digital control systems [1,[14][15][16][17][18][19][20][21], 2-D discrete switched systems [18,19,22] etc. The subject of 2-D uncertain systems has also received a significant amount of attention [11,16,17,23].…”

“…The zero solution of system (1)-(3) is globally asymptotically stable if one of the following conditions is satisfied:are defined in (15)-(19).…”