Stability analysis of switched systems with stable and unstable subsystems: An average dwell time approach

Exponential H∞ Filtering for Discrete‐Time Switched State‐Delay Systems Under Asynchronous Switching

“…12), respectively; thus the exponential stability follows from Lemma 1. Next, we show the weighted H• performance of the filtering error system Se.Assume without loss of generality that (tq) = i,(tq-1) = j, then f(tq + Dtq) = i, f (tq-1 + Dtq-1) = j.…”

“…A book [1] and a few papers [2][3][4] are examples of excellent surveys on the advances of switched systems. The typical issues studied on switched systems include observability and controllability [5][6][7], stability and stabilization [8][9][10][11][12][13][14][15][16][17][18][19][20], and filtering design [21][22][23][24]. Two logical rules, the state-dependent switching law and average dwell time switching law are often adopted [8][9][10][11][12][13].…”

“…The typical issues studied on switched systems include observability and controllability [5][6][7], stability and stabilization [8][9][10][11][12][13][14][15][16][17][18][19][20], and filtering design [21][22][23][24]. Two logical rules, the state-dependent switching law and average dwell time switching law are often adopted [8][9][10][11][12][13]. The tools and techniques for analysis and synthesis of switched control systems are typically based on common Lyapunov functions or multiple Lyapunov functions [14][15][16][17][18][19][20][21][22][23][24].…”

Determining Dissipativity of Switched Nonlinear Systems Using Linearization

“…Switched systems that contain a finite number of subsystems and a switching signal coordinating switching between them have attracted extensive attention in recent decades [1][2][3][4]. Because the solutions of switched systems depend on both the system's initial conditions and the switching strategies, the behaviors of switched systems are quite different from those of non-switched systems.…”

Stabilization of Discrete‐time Switched Systems with State Constraints Based on Mode‐Dependent Average Dwell Time

“…Among these studies, stability is a crucial and fundamental problem. It has been recognized that average dwell time (ADT) is more flexible and efficient in the stability problem of switched systems [12,13]. In addition, there some prolongations of the ADT have appeared [14][15][16][17].…”