Guaranteed performance cost control over Quality-of-Service networks

The communication quality has a strong effect on the stability and control performance of a networked control system (NCS). In order to achieve superior control performance, in general, high communication quality is desired. This might, however, be costly from a network point of view. This paper aims at finding a trade-off between control performance and network cost by exploiting the Quality-of-Service (QoS) concept. The network-induced time delay is considered as QoS parameter and modeled by a Markov process; its transition generator is assumed to be adjustable. The resulting system is a Markovian jump linear system (MJLS) with mode-dependent delays. A delay-dependent stability condition ensuring exponential mean-square stability is established. This is achieved together with an upper bound for the expected control performance by using a stochastic Lyapunov-Krasovskii functional. In addition, a perturbation upper bound for the Markov process transition generator is determined such that the resulting NCS is still stable and has guaranteed control performance. A trade-off between the control performance and network cost is achieved by optimizing the Markov process transition generator within this stabilizing perturbation range. The performance benefit of the proposed control concept is demonstrated in a numerical example.