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首页> 外文期刊>International Journal of Robust and Nonlinear Control >Robust global controller design for discrete-time descriptor systems with multiple time-varying delays
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Robust global controller design for discrete-time descriptor systems with multiple time-varying delays

机译：具有多个时变延迟的离散时间描述符系统的强大全局控制器设计

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摘要

Descriptor systems are ubiquitous in many complex practical systems including spacecraft, electrical networks, economic systems, robotic, vibrational, and structural systems. Time delays are ubiquitous in those complex systems. If not addressed properly at the control design stage, they will result in singularities such as oscillation, instability, degraded performance. This article proposes a novel linear matrix inequality (LMI)-based global sliding mode control (GSMC) approach for uncertain discrete-time descriptor systems with multiple time-varying delays. Strict LMI conditions are established based on free-weighting matrices and the Lyapunov-Krasovskii functional to guarantee admissible closed-loop dynamics, that is, regular, causal, and stable. The sufficient condition for the asymptotic stability of the sliding mode dynamics is obtained based on the Lyapunov stability theorem and LMI constraint. The GSMC approach is then formulated based on a global sliding surface to ensure robust performance of the closed-loop system against parametric uncertainties and time delays, while eliminating the reaching phase. The global sliding surface ensures robust performance without the need for a reaching phase, thus establishing sliding around the surface right from the beginning and reducing the control effort. The effectiveness and validity of the proposed approach is assessed using a numerical example.
机译：描述符系统在许多复杂的实际系统中普遍存在，包括航天器，电网，经济系统，机器人，振动和结构系统。在这些复杂的系统中，时间延迟普遍存在。如果没有在控制设计阶段正确解决，它们将导致奇点，如振荡，不稳定，性能下降。本文提出了基于具有多个时变延迟的不确定离散时间描述符系统的新的线性矩阵不等式（LMI）的全局滑模控制（GSMC）方法。严格的LMI条件是基于自由加权矩阵和Lyapunov-Krasovskii功能，以保证可接受的闭环动态，即规律，因果和稳定。基于Lyapunov稳定性定理和LMI约束，获得了滑模动态的渐近稳定性的充分条件。然后基于全局滑动表面配制GSMC方法，以确保闭环系统免受参数的不确定性和时间延迟的鲁棒性能，同时消除了达阶段。全局滑动表面可确保不需要到达阶段的稳健性能，从而从开始并降低控制工作，在表面上建立滑动。使用数值示例评估所提出方法的有效性和有效性。

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