On stability of linear and weakly nonlinear switched systems with time delay

Stability of Stochastic Differential Switching Systems with Time-Delay and Impulsive Effects

“…In addition, delay is also considered in many models. In [13,14], the authors established several criteria on exponential stability for nonlinear systems with time delay by using multiple Lyapunov function technique and a dwell-time approach. Recently, Pu et al considered the problem of stability of switching delay systems in [1,15].…”

“…For example, the model become a hybrid impulsive and switching NN model without stochastic effects (see [13][14][15][16]26]). If ( ) ( , ( − )) = 0, the model is a linear switching system considered in [3,4].…”

Asymptotic behavior of switched delay systems with nonlinear disturbances

“…The theory of switched systems has historically assumed a position of great importance in systems theory due to their strong engineering backgrounds (e.g. [1,2]), and has been studied extensively in recent years [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].…”

“…For the switched linear systems under arbitrary switching, common quadratic Lyapunov functions (or switched quadratic Lyapunov functions) were employed to investigate the asymptotic stability (see [7]). In [12], Alwan and Liu studied the linear and weakly nonlinear switched delay systems and obtained several exponential stability criteria by using multiple Lyapunov functions technique and dwell-time approach. Some necessary and sufficient conditions were also provided to ensure the asymptotic stability of switched linear systems under arbitrary switching laws [8].…”

Reduced-order fault detection filter design for switched nonlinear systems with time delay

“…Therefore, switched systems with time delay have a strong engineering background. Many results on switched delay systems which focus on, for instance, stability analysis [20][21][22][23], control and filtering [24][25][26][27], have been reported. While some other topics, such as fault detection, on this area are still open and challenging [28,29].…”