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Stabilizing transmission intervals and delays for linear time-varying control systems: The large delay case

The goal of this paper is to compute transmission intervals and delays that provably stabilize Linear Time-Varying (LTV) control systems in the presence of disturbances. In other words, given some signal delay existent in a control system, we determine rates at which information between the controller and plant need to be exchanged such that the closed-loop system is stable (in some appropriate sense). Depending on information noise and disturbances, the computed transmission intervals lead to stability, asymptotic stability and Lp-stability with bias. The proposed notion of Lp-stability with bias integrates noisy information into our stability analysis. The salient feature of our emulation-based methodology is the consideration of delays that are greater than transmission intervals. This feature stems from impulsive delayed system modeling and Lyapunov-Razumikhin techniques employed in the paper. Our methodology is demonstrated on the benchmark problem of batch reactor and compared with a related work.