The effect of coupling conditions on the stability of bimodal systems inR3

Abstract

a b s t r a c tThis paper investigates the global asymptotic stability of a class of bimodal piecewise linear systems in R 3 . The approach taken allows the vector field to be discontinuous on the switching plane. In this framework, verifiable necessary and sufficient conditions are proposed for global asymptotic stability of bimodal systems being considered. It is further shown that the way the subsystems are coupled on the switching plane plays a crucial role on global asymptotic stability. Along this line, it is demonstrated that a constant (which is called the coupling constant in the paper) can be changed without changing the eigenvalues of subsystems and this change can make bimodal system stable or unstable.

Well posedness conditions for planar conewise linear systems

“…CLS has been investigated from many different aspects in recent years, like well posedness (Imura and Van der Schaft, 2000; Şahan and Eldem, 2015; Thuan and Çamlibel, 2014; Xia, 2002); stability (Araposthatis and Broucke, 2007; Eldem and Oner, 2015; Eldem and Şahan, 2014, 2016; Pachter and Jacobson, 1981; Shen et al, 2009; Zhendong and Shuzhi, 2011); control (Çamlibel et al, 2008; Heemels et al, 2010) and observability (Çamlibel et al, 2006; Shen, 2010). Many of these works assume that the system has a continuous vector field on the switching boundary, which resolves the issue of well posedness.…”

Coupled Least Squares Identification Algorithms for Multivariate Output-Error Systems

“…The coupling identification concept is useful for simplifying the parameter estimation of the coupled parameter multivariable systems [23]. It is based on the coupled relationship of the parameter estimates between the subsystems of a multivariable system [24][25][26]. The purpose of the coupling identification is to reduce the redundant estimation of the subsystem parameter vectors and to avoid computing the matrix inversion of the RLS algorithm.…”