IEEE Trans Cybern. 2018 Oct;48(10):2783-2794. doi: 10.1109/TCYB.2017.2750221. Epub 2017 Sep 19.
In this paper, a delay-dependent algebraic Riccati equation (DARE) approach is developed to study the meansquare stabilization problem for continuous-time networked control systems. Different from most previous studies that information transmission can be performed with zero delay and infinite precision, this paper presents a basic constraint that the designed control signal is transmitted over a delayed communication channel, where signal attenuation and transmission delay occur simultaneously. The innovative contributions of this paper are threefold. First, we propose a necessary and sufficient stabilizing condition in terms of a unique positive definite solution to a DARE with Q > 0 and R > 0. In accordance with this result, we derive the Lyapunov/spectrum stabilizing criterion. Second, we apply the operator spectrum theory to study the stabilizing solution to a more general DARE with Q ≥ 0 and R > 0. By defining a delay-dependent Lyapunov operator, we propose the existence theorem of the unique stabilizing solution. It is shown that the stabilizing solution, if it exists, is unique and coincides with a maximal solution. Third, as an application, we derive the explicit maximal allowable delay bound for a scalar system. To confirm the validity of our theoretic results, two illustrative examples are included in this paper.
本文提出了一种时滞相关代数黎卡提方程（DARE）方法，用于研究连续时间网络控制系统的均方镇定问题。与大多数先前的研究不同，这些研究假设信息传输可以无延迟和无限精度进行，本文提出了一个基本约束，即设计的控制信号通过具有信号衰减和传输延迟的延迟通信信道传输。本文的创新贡献有三点。首先，我们提出了一个必要和充分的稳定条件，以一个具有 Q>0 和 R>0 的 DARE 的唯一正定解的形式给出。根据这一结果，我们推导出了 Lyapunov/谱稳定判据。其次，我们应用算子谱理论研究了更一般的 Q≥0 和 R>0 的 DARE 的稳定解。通过定义一个时滞相关的 Lyapunov 算子，我们提出了唯一稳定解的存在性定理。结果表明，如果存在稳定解，则它是唯一的，并且与最大解一致。第三，作为应用，我们推导出了标量系统的最大允许时滞界限的显式表达式。为了验证我们的理论结果的有效性，本文包含了两个说明性的例子。
