Networked Control Systems With Communication Constraints: Tradeoffs Between Transmission Intervals, Delays and Performance

There are many communication imperfections in networked control systems (NCS) such as varying transmission delays, varying sampling/transmission intervals, packet loss, communication constraints and quantization effects. Most of the available literature on NCS focuses on only some of these aspects, while ignoring the others. In this paper we present a general framework that incorporates communication constraints, varying transmission intervals and varying delays. Based on a newly developed NCS model including all these network phenomena, we will provide an explicit construction of a continuum of Lyapunov functions. Based on this continuum of Lyapunov functions we will derive bounds on the maximally allowable transmission interval (MATI) and the maximally allowable delay (MAD) that guarantee stability of the NCS in the presence of communication constraints. The developed theory includes recently improved results for delay-free NCS as a special case. After considering stability, we also study semi-global practical stability (under weaker conditions) and performance of the NCS in terms of Lp gains from disturbance inputs to controlled outputs. The developed results lead to tradeoff curves between MATI, MAD and performance gains that depend on the used protocol. These tradeoff curves provide quantitative information that supports the network designer when selecting appropriate networks and protocols guaranteeing stability and a desirable level of performance, while being robust to specified variations in delays and transmission intervals. The complete design procedure will be illustrated using a benchmark example.