离散多时滞广义不确定系统的变结构控制

VARIABLE STRUCTURE CONTROL OF DISCRETE UNCERTAIN MULTIPLE TIME-DELAYS SINGULAR SYSTEM

研究了线性离散多时滞广义不确定系统的变结构控制的综合与设计问题,首先引入了一种新的受限系统等价分解形式,把所给的系统分解成两个低维的子系统:一个是不带控制项的差分系统;一个是带有控制项的差分系统,其次,根据上面的分解形式及离散时滞广义系统鲁棒稳定性的有关结果,设计了带有差分补偿器的切换函数,使得系统在准切换流形上的运动渐近稳定,然后在不确定项有界的条件下,设计了离散变结构控制律,使得在此控制律的作用下,系统从状态空间中任意一点出发的解的轨迹,于有限步内或者到达准切换流形,此后在准切换流形上渐近滑向原点;或者进入准切换流形的一个小邻域内,并稳定于原点邻域内的一个小的抖振,最后给出了数值例子以说明该综合设计方法的可行性与简便性。

Synthesis and design of variable structure controller for linear discrete uncertain multiple time-delays singular system is studied. Firstly, a new restricted system equivalent form is developed and the system is decomposed into two low dimensional subsystems： one is a difference system without input; another is a difference system with input. Secondly, based on the above decomposition and some results on Robust stability of discrete time-delay singular systems, a switching function with difference compensator is designed, which guarantees the movement of the system is asymptotically stable in quasi-switching manifold. Thirdly, under assumption that the uncertain part is bounded, a variable structure controller is designed, which can force solution trajectory of the system either to arrive at the quasi-switching manifold in finite steps and ultimately slide to zero on the quasi-switching manifold or to enter into a small neighborhood of the quasi-switching manifold in finite steps and stablly convergent to a small chattering in the neighborhood. Finally, a numerical example is given to demonstrate feasibility and simplicity of the design method.