论文标题
延迟对常规线性系统的补偿
Delay Compensation for Regular Linear Systems
论文作者
论文摘要
这是四个系列论文的第三部分，旨在延迟对抽象线性系统的延迟补偿（a，b，c）。研究了输入延迟和输出延迟。我们首先提出了一个完整的状态反馈控制，以使用输入延迟稳定系统（a，b），然后根据延迟输出设计系统（A，C）的类似Luenberger的观察者。我们在常规线性系统的框架中制定延迟补偿。开发的方法建立在与Sylvester操作员方程相关的上限三角变换上。发现系统（-a，b）/（-a，-c）的可控性/可观察性图恰好是相应的Sylvester方程的解决方案。直接的结果，反馈法和国家观察者都可以以操作员形式明确表示。在不使用Lyapunov功能方法的情况下，建立了所得闭环系统和观察误差的指数收敛的指数稳定性。理论结果通过基准一维波方程的延迟补偿来验证。
This is the third part of four series papers, aiming at the delay compensation for the abstract linear system (A,B,C). Both the input delay and output delay are investigated. We first propose a full state feedback control to stabilize the system (A,B) with input delay and then design a Luenberger-like observer for the system (A,C) in terms of the delayed output. We formulate the delay compensation in the framework of regular linear systems. The developed approach builds upon an upper-block-triangle transform that is associated with a Sylvester operator equation. It is found that the controllability/observability map of system (-A,B)/(-A,-C) happens to be the solution of the corresponding Sylvester equation. As an immediate consequence, both the feedback law and the state observer can be expressed explicitly in the operator form. The exponential stability of the resulting closed-loop system and the exponential convergence of the observation error are established without using the Lyapunov functional approach. The theoretical results are validated through the delay compensation for a benchmark one-dimensional wave equation.
