A Stability Criterion for Networked Control Systems With Packetized Transmissions

Abstract

A networked output feedback loop subject to packetized transmissions of the output signal is considered. Based on the small gain theorem, an easy-to-use stability criterion covering two important cases is presented. In the first case a packet numbering mechanism is employed whereas in the second case neither packet numbering nor synchronization between sender and receiver is assumed. The analysis makes use of acausal subsystems and deduces the optimal constant time delay that should be used in a nominal controller design such that additional packet delay variations introduced by the network are maximized. A simulation example of a networked control system with a filtered Smith predictor illustrates the application of the proposed criterion and compares the results to different approaches from literature.

A less‐conservative stability criterion for networked control systems with time‐varying packet delays

“…Figure A.2 extends the analysis to different̂N , T and acausal delays A , where also the minimal delay − A and maximal delaŷN − A are indicated. All resulting delay patterns and output sequences show a similar structure as for the causal case [11], with the important differences that: (i) a maximal relative delaȳ A.2 Protocol  3 The calculation of * is more demanding for protocol  3 , because the delay patterns from the previous section only partially reproduce gains T , for example for  3 and A =̂N . This is visualized in Figure A.11 using blue plus signs.…”

“…Remark 5. For the causal case, that is for A = 0, one obtains the same conditions as (i) in [11] for a unity feedback loop [12] for a NCS with a filtered Smith predictor, R(z…”

“…In [12], a robust stability criterion is presented as well, which allows to account for uncertain plant models in feedback loops with variable packet delays. However, the results from [11] and [12] might be conservative. Consequently, the contributions of the present paper are: FIGURE 1 Feedback loop that is closed by means of a communication network with variable time delays j for the transmitted packets j (a) The existing SGT-based approaches are enhanced to get a less conservative stability criterion.…”

From classical to Networked Control: Retrofitting the Concept of Smith Predictors

“…A way to include protocols like P 1 and P 2 has been proposed in [33]. This work is extended in the following for networked feedback loops with filtered Smith predictors (see Fig.…”

“…As a basis for the present work, the small gain [31], [32] based stability criterion for networked feedback loops with bounded time-varying delays presented in [33] is used. The present work extends this approach with respect to several aspects.…”