二维切换系统FM状态空间模型的耗散稳定性分析与镇定控制

Dissipativity stability analysis and stabilization control for 2D switched FM systems

针对二维切换系统的Fornasini-Marchesini(FM)状态空间模型,对系统耗散稳定性以及耗散镇定控制器的设计问题进行研究.首先,根据系统模型的特点,给出了二维系统(T,S,R)-δ-耗散性的定义,并提出二维切换系统渐近稳定和满足(T,S,R)-δ-耗散性的充分条件;然后利用稳定性条件和投影引理,设计了二维(T,S,R)-δ-耗散状态反馈控制器.最后,通过一个数值实例来验证所设计控制器的有效性.

This paper investigates the dissipative stability analysis and control problem for the two-dimensional(2-D)switched Fornasini-Marchesini local state-space(FMLSS)model.Firstly,the definition of 2-D(T,S,R)-δ-dissipativity is introduced for the 2-D FM systems.Secondly,the sufficient condition to guarantee the asymptotical stability and(T,S,R)-δ-dissipativity of the 2-D switched FM systems is proposed.Then the 2-D(T,S,R)-δ-dissipative state-feedback controller is designed based on the obtained dissipative stability condition and the projection lemma technique.Finally,the effectiveness of the proposed method is illustrated via a numerical example.