Title: Dynamical State Feedback Control for Linear Input Delay Systems, Part I: Dissipative Stabilization via Semidefinite Programming Show Chinese title

Title: 线性输入延迟系统的动态状态反馈控制，第一部分：通过半定规划的耗散稳定化

Abstract: We propose an SDP-based framework to address the stabilization of input delay systems while taking into account dissipative constraints. A key to our approach is the introduction of the concept of parameterized linear dynamical state feedbacks (LDSFs), which draws inspiration from recent advancements in the analyses of distributed delays. Importantly, the parameterized LDSFs generalize conventional predictor controllers, where the interpretation of state prediction is concealed and their degree of parameterization can be increased by adjusting the integral kernels. A sufficient condition for the existence of dissipative LDSFs is formulated as matrix inequalities by constructing a complete type Krasovski\u{\i} functional. To solve the bilinear matrix inequality in the synthesis condition, we employ an off-line inner convex approximation algorithm that can be initialized using the gains of predictor controllers obtained via explicit construction. Finally, the unknowns of our dissipative LTDS can be directly obtained by solving convex semidefinite programs. Numerical examples and simulations were experimented to demonstrate the validity and effectiveness of our methodology. Show Chinese abstract

Abstract: 我们提出一个基于SDP的框架，以解决输入延迟系统的稳定性问题，同时考虑耗散约束。 我们方法的关键是引入参数化线性动态状态反馈（LDSFs）的概念，这受到分布式延迟分析最近进展的启发。 重要的是，参数化LDSFs推广了传统的预测控制器，其中状态预测的解释被隐藏，并且通过调整积分核可以增加其参数化程度。 通过构建一个完整的Krasovskiĭ泛函，耗散LDSFs存在的充分条件被表述为矩阵不等式。 为了求解合成条件中的双线性矩阵不等式，我们采用了一个离线内凸近似算法，该算法可以通过通过显式构造获得的预测控制器增益进行初始化。 最后，我们耗散LTDS中的未知数可以直接通过求解凸半定规划得到。 数值示例和仿真被进行以证明我们方法的有效性和有效性。