凸多面体不确定Delta算子切换系统的二次稳定性

Quadratic Stabilizability of Delta Operator Switching Systems with Polytopic Uncertainties

研究不确定Delta算子切换系统的二次稳定性问题,其子系统矩阵表示为顶点矩阵的线性凸组合。基于δ域的Lyapunov稳定性理论,在不要求子系统稳定的情况下,找到一族非负标量和一个公共的正定矩阵,使Delta算子切换系统在状态依赖的切换律下是二次稳定的,切换律由公共的正定矩阵给出。数值算例检验了方法的有效性。

The problem of quadratic stabilizability of Delta operator switching systems is studied.The matrix of the subsystems is expressed as a polytopic linear combination of vertex matrices.Based on Lyapunov stability theory,a family of non-negative scalars and a common positive definite matrix are found without requiring quadratic stabilization of subsystems,which makes Delta operator switching systems quadratic stabilizability under state-dependent switching laws.It is to propose the switching rules by using the obtained common positive definite matrix.An example is given to illustrate the effectiveness of the proposed method.