二次型耗散线性离散系统的鲁棒性分析与控制

考虑一类不确定离散多变量系统的鲁棒二次型耗散性分析和控制,其中各不确定参数矩阵具有线性分式形式.首先对确定系统建立二次型耗散性与正实性之间的等价关系,由此导出线性系统二次型耗散的充分必要条件;然后证明不确定系统的鲁棒耗散性分析和控制可转化为确定系统的耗散性分析和设计,给出了这类不确定系统鲁棒耗散的充分必要条件以及鲁棒耗散控制问题的线性矩阵不等式解法.所得结果可将H∞控制与正实控制统一起来,提供一种较为灵活、保守性较小的系统设计方法.仿真例子说明了所提方法的有效性.

Robust quadratic dissipative analysis and control for discrete-time systems

The robust quadratic dissipative control problem for a class of uncertain discrete-time systems is (considered) where the uncertainties are expressed in a linear fractional form. Equivalence between quadratic (dissipativeness) and positive realness is established, and necessary and sufficient (conditions) are derived for (linear) systems to be strict quadratic dissipative. It is shown that the quadratic dissipative analysis and control of the (uncertain) systems can be reduced to those of related systems without uncertainties. Necessary and sufficient (conditions) are obtained for the uncertain systems to be robust quadratic dissipative. The robust quadratic dissipative control problem can be solved using an LMI (approach.) An example shows the applicability of the proposed (approach.)