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针对分数阶不确定系统,讨论了输出反馈镇定问题.分别针对阶数为0<α<1和1α<2两种情况进行讨论,基于输出反馈控制器的设计,并利用系统特征方程的根、矩阵Kronecker积,得出系统的李亚普诺夫全局稳定性条件.最后利用Schur补引理以及矩阵奇异值分解形式,将系统稳定性条件以线性矩阵不等式(LMI)给出,易于求解增益矩阵.
For the fractional order uncertain systems, the output feedback stabilization problem is discussed. Two orders of 0 <α <1 and 1α <2 are discussed respectively. Based on the design of the output feedback controller and using the root of the system characteristic equation, Matrix Kronecker product, the system Lyapunov global stability conditions are obtained.Finally, the system stability conditions are given by linear matrix inequality (LMI) using Schur complement and matrix singular value decomposition, which makes it easy to solve the gain matrix.