Delay independent stability of linear switching systems with time delay

Abstract

We consider a switching system with time delay composed of a finite number of linear delay differential equations (DDEs). Each DDE consists of a sum of a linear ODE part and a linear DDE part. We study two particular cases: (a) all the ODE parts are stable and (b) all the ODE parts are unstable and determine conditions for delay independent stability. For case (a), we extend a standard result of linear DDEs via the multiple Lyapunov function and functional methods. For case (b) the standard DDE result is not directly applicable, however, we are able to obtain uniform asymptotic stability using the single Lyapunov function and functional methods.

Reliable H ∞ Filtering for Discrete-Time Switched Singular Systems with Time-Varying Delay

“…Pre-and post-multiplying diag{I (5n+p)×(5n+p) , H −1 1 , H −1 2 , H −1 2 , I q×q } and its transpose to (12), then (32) leads to (31). This completes the proof.…”

“…However, the problem for the global existence and uniqueness of the solution to system (1) with w k = 0 is much more complicated than that of the non-switched case, mainly because the modes switching should be counted as a solution or as a part of solution in determining the global existence and uniqueness. Using the methods in [12], if system (1) with w k = 0 is finite time finite switching, the solution to the system is bounded for each σ (k) = i ∈ L, and there exists a unique mode transition at each switching moment, then we may expect the global existence and uniqueness of the solution to the system. For more details of the global existence and uniqueness of the solution to the switched systems, we refer the readers to [12,16].…”

“…Using the methods in [12], if system (1) with w k = 0 is finite time finite switching, the solution to the system is bounded for each σ (k) = i ∈ L, and there exists a unique mode transition at each switching moment, then we may expect the global existence and uniqueness of the solution to the system. For more details of the global existence and uniqueness of the solution to the switched systems, we refer the readers to [12,16].…”

Stability of a class of linear switching systems with time delay

“…Using the Method of Steps [22,23] it is straightforward to show [24] that there is a unique function x :…”

Practical Uniform Stability of Nonlinear Differential Delay Equations

“…Recently, improved performance have been reported by using Lyapunov-Krasovskii methods and linear matrix inequalities (LMI's) techniques, see [2,3,5,6,7,8,15,17,19,23,24].…”