A Lyapunov Proof of an Improved Maximum Allowable Transfer Interval for Networked Control Systems

Abstract

Abstract-Simple Lyapunov proofs are given for an improved (relative to previous results that have appeared in the literature) bound on the maximum allowable transfer interval to guarantee global asymptotic or exponential stability in networked control systems and also for semiglobal practical asymptotic stability with respect to the length of the maximum allowable transfer interval.

Input-to-state stabilizing event-triggered control for linear systems with output quantization

“…Note that whenλ = λ in (16), we recover the MATI bound of the time-triggered controllers in [4]. We observe that, in view of (16), whenλ ∈ [λ, λ −1 ) is increased, the guaranteed minimum time T between two transmission instants will be reduced.…”

“…The controller (5) is designed by an emulation approach in the sense that we assume that the closed-loop system given by (4) and (5) is stable when the effects of both the quantization and the network are absent, i.e. whenŷ q = y.…”

“…Assumption 2 establishes an L 2 -gain stability property for the systemẋ = A 1 x + B 1 e + E 1 w from (|e|, |w|) to (|A 2 x + B 2 e + E 2 w|, |y|), see also, e.g., [1], [4], [5].…”

“…The time T (λ,λ, γ,L) corresponds to the maximally allowable transmission interval (MATI) of time-triggered controllers [4]. The expression of T in (16), we drop the arguments of T for brevity, is derived as the time T it takes for a decreasing function φ : R 0 → R 0 to decrease from φ(0) = λ −1 to φ(T ) =λ, where φ has the dynamics, see also [4] …”

“…Property (3) means that chatteringlike behaviour between the zoom-in and the zoom-out stages does not occur. Property (4) shows that the zoom variable µ remains bounded and the values of κ in (y, µ) and κ out (y, µ), which will be transmitted, are finite. Finally, property (5) means that the time domain of solutions to system (11)- (12) is unbounded.…”