An Average Allowable Transmission Interval Condition for the Stability of Networked Control Systems
S.H.J. Heijmans, Romain Postoyan, Dragan Nešić, W.P.M.H. Heemels
Abstract
A popular design framework for networked control systems (NCSs) is the emulation-based approach combined with Lyapunov-based analysis techniques for hybrid systems. In virtually all papers that use this framework, bounds in terms of the maximal allowable transmission interval (MATI) are provided to guarantee stability, and performance properties of the NCS. However, having only such a MATI condition is rather restrictive, and unrealistic in practice due to various network effects such as packet losses, leading to conservative bounds. In this article, we therefore consider an alternative condition on the communication instants to better capture the time-varying properties of the transmission intervals. In particular, we propose, in addition to the existence of a MATI, to also impose a bound on the average allowable transmission interval, expressed in terms of a reverse average dwell-time condition on the transmission intervals. We demonstrate by means of a novel Lyapunov-based analysis that stability of the NCS can still be guaranteed under this different condition on the transmission intervals, which can, in addition, lead to a significant improvement of the MATI. The strengths of these new results will be illustrated on a numerical example.