Containability With Event-Based Sampling for Scalar Systems With Time-Varying Delay and Uncertainty

This letter studies unstable scalar continuous-time systems with uncertain parameters that are controlled over a network with finite capacity with possible uncertain, but uniformly bounded, time-varying transmission delays. While the decoder and controller are assumed to be static and memoryless, we are particularly interested in the role of the sampling mechanism that is allowed to be event-based, i.e., dependent on the state. The control goal is to guarantee containability and to characterize the minimal requirements in terms of asymptotic average bit and triggering rates for satisfying this objective. Our first investigation neglects the transmission delay and focuses on the importance of the alphabet due to uncertain system parameters. The remainder of the study characterizes the general case, by deriving general bounds on the allowable delay and the asymptotic average bit and triggering rates for two alphabets. This letter closes with a comparison of the derived bounds and conclusions that can be drawn regarding the choice of the alphabet.