SCIENCE CHINA Information Sciences, Volume 61 , Issue 12 : 122201(2018) https://doi.org/10.1007/s11432-017-9318-2

## IQC based robust stability verification for a networked system with communication delays

Zhike WANG 1,2,*,
• AcceptedNov 30, 2017
• PublishedNov 22, 2018
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### Abstract

In this paper, we consider robust stability analysis of a networked system with uncertain communication delays.Each of its subsystems can have different dynamics, and interconnections among its subsystemsare arbitrary. It is assumed that there exists an uncertain but constant delay in each communicationchannel. Using the so called integral quadratic constraint (IQC) technique, a sufficient robust stability conditionis derived utilizing a sparseness assumption of the interconnections, and a set of decoupled robustness conditionsare further derived which depend only on parameters of each subsystem, the subsystem connection matrix (SCM) and theselected IQC multipliers. These characteristics result in an evident improvement of computational efficiency forrobustness verification of the networked system with delay uncertainties, which is illustrated by some numerical results.

### Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. 61573209, 61733008).

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• Figure 1

Transformed LFT model structure of system $\bf~\Sigma$.

• Figure 2

Stability analysis structure under the IQC framework.

• Figure 3

Averaged computation time of the robustness verifications.

• Figure 4

Estimated boundary for the stability region in $\tau_1$-$\tau_2$ plain.

• Table 1   Computation time for robust stability verification
 Subsystem Average CPU time (s) Standard deviation (s) number $N$ LMI (lumped) Theorem 1 Theorem 2 LMI (lumped) Theorem 1 Theorem 2 2 0.0184 0.0343 0.0330 0.0316 0.0076 0.0389 4 0.1539 0.1834 0.0607 0.0472 0.0293 0.0395 6 0.6426 0.7331 0.0911 0.0982 0.0921 0.0413 8 1.9633 1.7141 0.1207 0.3007 0.2309 0.0430 10 5.1660 4.0375 0.1692 0.4497 0.5571 0.0532 12 12.5412 8.6380 0.1964 1.1057 1.0417 0.0551 14 25.8146 16.3217 0.2293 1.8817 1.2748 0.0579 16 53.4153 26.5453 0.2654 1.8952 1.3492 0.0598 18 90.0755 41.5946 0.2952 0.8409 1.5985 0.0623 20 148.5057 60.6832 0.3255 1.5072 1.5344 0.0610 30 1164.2107 247.0348 0.4883 15.8555 6.5307 0.0669

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