Self-Triggered Stabilization of Discrete-Time Linear Systems With Quantized State Measurements

Abstract

We study the self-triggered stabilization of discretetime linear systems with quantized state measurements. In the networked control system we consider, sensors may be spatially distributed and be connected to a self-triggering mechanism through finite data-rate channels. Each sensor independently encodes its measurements and sends them to the self-triggering mechanism. The self-triggering mechanism integrates quantized measurement data and then computes sampling times. Assuming that the closed-loop system is stable in the absence of quantization and self-triggered sampling, we propose a joint design method of an encoding scheme and a self-triggering mechanism for stabilization. To deal with data inaccuracy due to quantization, the proposed self-triggering mechanism uses not only quantized data but also an upper bound of quantization errors, which is shared with a decoder.

Coding–Decoding-Based Sliding Mode Control for Markovian Jump Systems Under Constrained Bit Rate: An Adaptive Quantizer Approach

“…. , n), for any i ∈ S, h ∈ M, if there exist matrices K h ∈ R m×n , Qi > 0, Wi > 0, scalars ξ τ 2 > 0 satisfying the condition (28), ϑi > 0 satisfying (29) and…”

“…This network modeling is reasonable for many practical systems, wherein the sensor and the controller are usually connected via a wireless network with bandwidth constraints. While in controller-toactuator channel, the bandwidth of network is usually large enough to maintain the effectiveness of the control scheme or the controller and the actuator are connected by the wire as in [29], [30]. Actually, the control scheme proposed in this paper can be readily extended to the network modeling with the consideration of the CDP in both sensor-to-controller and controller-to-actuator channels.…”

“…The time and amplitude of the discrete signal are collected by severally sampling and quantizing the analog signal, while the coding process maps the discrete signal to binary number to facilitate the transmission [27]. The pioneering work on quantized control refers to [28] and recent results have been reported in [29], [30], for MJSs in [31]- [33]. In particular, asynchronous H∞ control of MJSs using detected-mode-based logarithmic quantizer has been reported in [32], the SMC of MJSs using dynamical uniform quantizer has been investigated in [33].…”