线性离散时滞系统的输出反馈镇定

Output feedback stabilization for discrete-time linear time-delay systems

针对一类带有区间时变时滞的线性离散系统,研究静态输出反馈镇定问题和动态输出反馈镇定问题。通过构造合适的Lyapunov函数,并使用Jensen不等式技术和时滞区间因子技术处理其差分,分别给出了系统可由静态输出反馈和动态输出反馈镇定的时滞依赖的充分条件。后使用矩阵分块技术从理论上证明了所给出的镇定判据比文献中已有的具有更小的保守性。对获得的理论结果进行了数值仿真,仿真结果既表明了所提出方法的正确性和可应用性,也说明了增加时滞区间因子数可以减少镇定判据的保守性。

For a class of discrete-time linear systems with an interval time-varying state delay, the stabili- zation problems via static output feedback and dynamic out feedback were considered. By constructing an appropriate Lyapunov function as well as using Jensen inequality technique and time-delay factor tech- nique, delay-dependent sufficient conditions of stabilizing the class of systems via static output feedback and dynamic out feedback were obtained, respectively. Then, by matrix-block technique, it is theoretical- ly shown that the proposed stabilization criteria are less conservative than ones in literature. Numerical simulations of the obtained theoretical results were presented, and the results of simulation show that not only the proposed approach is correct and applicable, but also the conservativeness of stabilization criteria is reduced as increasing the number of time-delay factors.