Observer-Based Bounded <i>H</i> _∞ Control for Shift-Varying Linear Repetitive Processes With Constrained Bit Rates Over a Finite Horizon

This technical correspondence examines the issue of observer-based bounded $H_{\infty }$ control for a kind of shift-varying linear repetitive process (LRP) over networks with constrained bit rates in the finite horizon. Unlike the previous researches that address (or avoid) the problem of limited network resources by designing different scheduling protocols, this study focuses on further reducing and optimizing the bandwidth utilization by introducing a bit rate constraint model. Thus, an encoding-decoding mechanism under the constrained bit rates is proposed based on the quantization method. In order to analyze the $H_{\infty }$ performance of the LRP and design an appropriate controller, the LRP is transformed into a shift-varying two-dimensional (2-D) Fornasini-Marchesini model. Sufficient conditions in recursive linear matrix inequalities are proposed to ensure that the extended system achieves a bounded $H_{\infty }$ performance over a finite horizon within the 2-D framework. Furthermore, a component-based strategy for allocating the bit rates is provided to expand the quantization region under the constraint of bit rates. Finally, the effectiveness of the proposed method is verified by a simulation example.