Quantized sliding mode control under hidden Markov digital block-fading channels

This paper investigates the problem of sliding mode control (SMC) design under the finite-state Markov digital block-fading channels. Before transmitting through the independent digital channels, the output measurements are first quantized through logarithmic quantizers. Then, p independent finite-state hidden Markov models are introduced to model the time-varying effects subject to error-free packet arrival rates. A new one-to-one mapping rule is proposed for reformulating p Markov chains into a new Markov chain. By means of the information from the mode detectors, we construct the detected mode-dependent state observer and the corresponding sliding mode controller. Both the exponential mean-square stability of the closed-loop system and the reachability of the specified sliding surface are analyzed through the fading mode-dependent Lyapunov function method. Furthermore, by adopting the binary genetic algorithm (GA), an optimizing quasi-sliding mode is further achieved. Finally, an illustrative example is provided to verify the effectiveness of the proposed method. (C) 2021 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.