Abstract
This paper investigates the closed-loop £ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> stability of two-dimensional (2-D) feedback systems across a digital communication network by introducing the tool of dissipativity. First, sampling of a continuous 2-D system is considered and an analytical characterization of the QSRdissipativity of the sampled system is presented. Next, the input-feedforward output-feedback passivity, a simplified form of QSR-dissipativity, is utilized to study the framework of feedback interconnection of two 2-D systems over networks. Then, the effects of signal quantization in communication links on dissipativity degradation of the 2-D feedback quantized system is analyzed. Additionally, an event-triggered mechanism is developed for 2-D networked control systems while maintaining £ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> stability of the closed-loop system. In the end, an illustrative example is provided.
Highlights
Two-dimensional (2-D) continuous systems arise naturally in a wide range of applications, where the system variables depend on two variables, such as time and distance, or height and width
We show that a large sampling period may lead to the sampled system becoming non-dissipative and for a linear continuous 2-D system, we provide a LMI-based sufficient condition to determine whether the sampled system is QSR-dissipative
By utilizing input-feedforward output-feedback passivity (IF-output feedback passive (OFP)), a simplified form of QSR-dissipativity, the second step is to analyze the effect of the quantization on the closed-loop L2 stability
Summary
Two-dimensional (2-D) continuous systems arise naturally in a wide range of applications, where the system variables depend on two variables, such as time and distance, or height and width. We choose a dissipativity based framework to analyze 2-D feedback systems across a digital network. Dissipativity (and its special case of passivity) are rather standard notions for 1-D systems [13] They provide an energy-based perspective for analysis and design, and relate strongly to Lyapunov and L2 stability theories [14]. The main contribution of this work is to present L2 stability analysis of 2-D continuous feedback systems across a digital network using dissipativitybased notions. For a symmetric matrix represented blockwise, off diagonal blocks are abbreviated with “*”
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