Sliding Mode Control of Uncertain Switched Systems via Length-Limited Coding Dynamic Quantization

This paper designs an online adjustment strategy for dynamic quantizer parameters and investigates the sliding mode control (SMC) problem for uncertain switched systems under a limited network communication bandwidth. Due to the limitation of the coding length in practical transmission, coding errors can significantly impact the system’s ideal performance. To address these issues, a dynamic quantizer is introduced to efficiently encode the system state while minimizing quantization error under the constraint of the finite code length. Additionally, a coding and decoding scheme based on dynamic quantization and a suitable sliding mode controller are designed to obtain a closed-loop switched system. Using Lyapunov functions and the average dwell time method, sufficient conditions are derived to guarantee the reachability of the sliding surface and the exponential ultimate bound (EUB) in the mean square for the closed-loop switched system, even in the presence of coding errors and data loss. The theoretical results are validated through numerical simulations, which demonstrate the effectiveness of the proposed approach.