Being a unique phenomenon in hybrid systems, mode switch is of fundamental importance in dynamic and control analysis. In this paper, we focus on global long-time switching and stability properties of conewise linear systems (CLSs), which are a class of linear hybrid systems subject to state-triggered switchings recently introduced for modeling piecewise linear systems. By exploiting the conic subdivision structure, the “simple switching behavior” of the CLSs is proved. The infinite-time mode switching behavior of the CLSs is shown to be critically dependent on two attracting cones associated with each mode; fundamental properties of such cones are investigated. Verifiable necessary and sufficient conditions are derived for the CLSs with infinite mode switches. Switch-free CLSs are also characterized by exploring the polyhedral structure and the global dynamical properties. The equivalence of asymptotic and exponential stability of the CLSs is established via the uniform asymptotic stability of the CLSs that in turn is proved by the continuous solution dependence on initial conditions. Finally, necessary and sufficient stability conditions are obtained for switch-free CLSs.

Keywords: variable structure systems, Lyapunov and other classical stabilities, asymptotic stability

@article{COCV_2010__16_3_764_0, author = {Shen, Jinglai and Han, Lanshan and Pang, Jong-Shi}, title = {Switching and stability properties of conewise linear systems}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {764--793}, publisher = {EDP-Sciences}, volume = {16}, number = {3}, year = {2010}, doi = {10.1051/cocv/2009021}, mrnumber = {2674636}, zbl = {1195.93028}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2009021/} }

TY - JOUR AU - Shen, Jinglai AU - Han, Lanshan AU - Pang, Jong-Shi TI - Switching and stability properties of conewise linear systems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2010 SP - 764 EP - 793 VL - 16 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2009021/ DO - 10.1051/cocv/2009021 LA - en ID - COCV_2010__16_3_764_0 ER -

%0 Journal Article %A Shen, Jinglai %A Han, Lanshan %A Pang, Jong-Shi %T Switching and stability properties of conewise linear systems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2010 %P 764-793 %V 16 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2009021/ %R 10.1051/cocv/2009021 %G en %F COCV_2010__16_3_764_0

Shen, Jinglai; Han, Lanshan; Pang, Jong-Shi. Switching and stability properties of conewise linear systems. ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 3, pp. 764-793. doi : 10.1051/cocv/2009021. http://archive.numdam.org/articles/10.1051/cocv/2009021/

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