Stability regions in the parameter space: D-decomposition revisited
Stability regions in the parameter space: D-decomposition revisited
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DOI：
10.1016/j.automatica.2005.08.010
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发表时间：
2006
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影响因子：
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通讯作者：
E. Gryazina;Boris Polyak
中科院分区：
文献类型：
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作者：
E. Gryazina;Boris Polyak
线性控制理论中具有挑战性的问题是描述提供系统稳定性的全部参数集（控制器系数或对象特性）。对于一个复参数或两个实参数和SISO系统（具有线性依赖于这些参数的特征多项式）的情况，可以使用所谓的d分解来图形化地解决问题。我们的目标是扩展该技术，并将其与通用M-Δ框架联系起来。用这种方法，我们研究了多项式的d分解的几何性质，并估计了根不变区域的数目。几个例子证实，这些估计是严格的。我们也扩展了矩阵情况下的d分解，即对于MIMO系统。例如，我们将参数k的实轴或复平面划分为矩阵A+kB稳定特征值数目不变的区域。类似的技术可以应用于双参数双输入双输出系统。
The challenging problem in linear control theory is to describe the total set of parameters (controller coefficients or plant characteristics) which provide stability of a system. For the case of one complex or two real parameters and SISO system (with a characteristic polynomial depending linearly on these parameters) the problem can be solved graphically by use of the so-called D-decomposition. Our goal is to extend the technique and to link it with general M-Δ framework. In this way we investigate the geometry of D-decomposition for polynomials and estimate the number of root invariant regions. Several examples verify that these estimates are tight. We also extend D-decomposition for the matrix case, i.e. for MIMO systems. For instance, we partition real axis or complex plane of the parameter k into regions with invariant number of stable eigenvalues of the matrix A+kB. Similar technique can be applied to double-input double-output systems with two parameters.