不确定非线性跳变系统滑模耗散控制

Sliding mode dissipative control for uncertain jumping nonlinear systems

针对既含有连续时间演化,又含有马尔可夫事件驱动的一类非线性不确定混杂动态跳变系统,研究相异滑模面上的耗散控制问题。对于跳变系统所具有的匹配的不确定性,可根据滑模控制理论,设计比例-积分多滑模面及相应滑模控制器。与此同时利用耗散控制理论并结合线性矩阵不等式,得到存在非线性和非匹配不确定性滑模面的无记忆状态耗散控制器。如此,系统滑模耗散控制器便可给出。最后数值事例验证定理的正确性。

The different sliding mode surface dissipative control problems are discussed for a class of Markov jump nonlinear systems with uncertainties. The systems involve both time-evolving and event driven mechanisms. In terms of sliding mode theory, different sliding mode surfaces and controllers are designed for the matched uncertainties. Dissipative control theory and linear matrix inequality are applied to sliding mode surface with nonlinear and unmatched uncertainties. Thereafter, the memoryless state feedback controllers are given. Finally, a sliding mode dissipative controllers are gained. A numerical example demonstrates the effect of the proposed design approach.