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针对一类含有分布时滞和不满足匹配条件的不确定中立型系统,通过利用Lya-punov稳定性理论和线性矩阵不等式(LMI)方法进行了滑模控制研究。首先,选取了依赖于当前状态和状态时滞的滑模面;设计了包含等效控制和非线性切换控制的滑模控制器使得系统满足滑模到达条件,即确保了系统在有限时间内到达滑模面。通过构造适当的Lyapunov函数,利用积分不等式技术,给出了闭环系统渐近稳定的充分条件。该充分条件通过采用虚拟反馈控制思想,结合状态反馈的极点配置方法,转换为线性矩阵不等式的形式,可通过Matlab中的LMI工具箱进行方便的求解。具体算例说明此方法的有效性。
For a class of uncertain neutral systems with distributed delays and matching conditions, the sliding mode control is studied by using the Lya-Punov stability theory and the linear matrix inequality (LMI) method. Firstly, the sliding mode surfaces which depend on the current state and the state delay are selected. A sliding mode controller with equivalent control and nonlinear switching control is designed so that the system satisfies the sliding mode arrival condition, that is, the system is ensured to reach within a limited time Slipform surface. By constructing the appropriate Lyapunov function and using integral inequality technique, the sufficient conditions for the asymptotic stability of the closed-loop system are given. This sufficient condition is transformed into the form of linear matrix inequality by adopting the idea of virtual feedback control combined with the pole placement of state feedback and can be easily solved by LMI toolbox in Matlab. The concrete example shows the validity of this method.