基于线性矩阵不等式的不确定关联系统的分散鲁棒镇定

Decentralized Robust Stabilization for Linear Uncertain Interconnected Systems Based on Linear Matrix Inequality

应用线性矩阵不等式 (L MI)方法研究不确定性关联大系统的分散鲁棒镇定问题。系统中不确定项具有数值界 ,可不满足匹配条件。基于不确定项的表达形式 ,给出了其可分散状态反馈镇定的充分条件 ,即一组 L MIs有解。在此基础上 ,通过求解一凸优化问题 ,提出了具有较小反馈增益的分散稳定化状态反馈控制律的设计方法。仿真示例说明了该方法的有效性和优越性。

The decentralized robust stabilization problem for large scale uncertain systems is studied by means of linear matrix inequality (LMI) approach. The uncertainty is bounded and may not satisfy the so called matching conditions. A sufficient condition for decentralized stabilization feedback control laws is derived. This condition is expressed as the solvability problem of linear matrix inequalities (LMIs). A convex optimization problem with LMI constraints is formulated to design a decentralized state feedback control with smaller gain parameters which enables the closed loop system asymptotically stable.