Robust stability for time-delay systems: the edge theorem and graphical tests
Robust stability for time-delay systems: the edge theorem and graphical tests
复制标题
DOI：
10.1109/cdc.1988.194276
复制
发表时间：
1988-12
期刊：
影响因子：
--
通讯作者：
M. Fu;A. Olbrot;M. Polis
中科院分区：
文献类型：
--
作者：
M. Fu;A. Olbrot;M. Polis
研究了一类特征方程为拟多项式多面体的不确定时滞系统的D-稳定性问题。他们的第一个结果表明，在对集合D的一个温和的假设下，拟多项式的多面体是D-稳定的当且仅当多面体的边是D-稳定的。这推广了A.C. Bartlett，et.等（1987）和M. Fu和B.R. Barmish（1988）关于多项式多面体的D-稳定性。第二个结果提供了一个基于极图的图形测试检查拟多项式的多面体的D-稳定性。在一个特殊的情况下，其中的垂直quasipolynomials是在一个因式分解的形式，图形测试进一步简化了一个特殊的映射。如示例所示，这里提供的图形测试在应用中非常有用，可以轻松处理具有许多不确定参数的示例。
The authors consider the D-stability problem for a class of uncertain delay systems where the characteristic equations involve a polytope of quasipolynomials. Their first result shows that under a mild assumption on the set D, a polytope of quasipolynomials is D-stable if and only if the edges of the polytope are D-stable. This extends the edge theorem developed by A.C. Bartlett, et. al. (1987) and M. Fu and B.R. Barmish (1988) for the D-stability of a polytope of polynomials. The second result provides a polar-plot-based graphical test for checking the D-stability of a polytope of quasipolynomials. In a special case in which the vertical quasipolynomials are in a factored form, the graphical test is further simplified by a special mapping. As shown in an example, the graphical tests provided here are quite useful in applications, making it possible to handle examples with many uncertain parameters easily.>