Exponential stability analysis and stabilization of switched delay systems

Stability of Switched Systems with Time-Varying Delays under State-Dependent Switching

“…) is a state-dependent switching rule which is generated by switching device [13]. Similar to [13][14][15][16][17][18][19][20][21][22][23], in this paper we also assume that there is no delay produced in switching device.…”

“…In [15][16][17][18][19], the researchers have also studied the stability of delayed switched systems under state-dependent switchings. However, these results assume that there exists a Hurwitz linear convex combination of A p + B p (or A p ).…”

“…Its basic idea can be summarized as follows: (a) divide the state space into different switching regions; (b) determine the index of activated subsystems for each switching region; (c) derive the stability conditions for switched systems under the designed switching rule. Under the assumption that there exists a Hurwitz convex combination of system matrices, the state-dependent switching rules have been designed via the regional partition of state space and some significant stability results have been deduced by common Lyapunov function (functional) in [13][14][15][16][17][18][19]. Remarkably, this assumption is a severe prerequisite.…”

“…Up to now, the literatures on the stability of delayed switched systems with statedependent switching rules include [15][16][17][18][19][20][21]27]. However, the assumption that there exists a Hurwitz convex combination of system matrices is serious, which affects the effectiveness of stability results presented in [15][16][17][18][19][20]. The additional condition on strict completeness of regional partition makes it difficult to get appropriate switching regions [21].…”

Control for Time‐Varying Delay Systems by Integrating Semi‐Discretization and Hysteresis‐Based Switching

“…See [29][30][31][32] for examples. Switched linear systems with time-varying delay has also been studied extensively [33][34][35][36][37]. Among those studies, exponential stability was particularly focused when interval time-varying delays are present in the system.…”