Robust Fixed-Order Controller Design for Uncertain Systems With Generalized Common Lyapunov Strictly Positive Realness Characterization
本文针对单输入单输出区间不确定多面体系统，提出一种鲁棒固定阶控制器设计方法，利用广义公共李雅普诺夫严格正实性将鲁棒稳定性和性能指标转化为线性矩阵不等式条件，仅需求解五个LMI即可保证性能，显著降低计算负担。
This article investigates the design of a robust fixed-order controller for single-input–single-output (SISO) polytopic systems with interval uncertainties, with the aim that the closed-loop stability is appropriately ensured and the performance specifications on sensitivity shaping are conformed in a specific finite frequency range. Utilizing the notion of generalized common Lyapunov strictly positive realness (CL-SPRness), the equivalence between strictly positive realness (SPRness) and strictly bounded realness (SBRness) is established; and then, the specifications on robust stability and performance are transformed into the SPRness of newly constructed systems and further characterized in the framework of linear matrix inequality (LMI) conditions. The proposed methodology avoids the tedious yet mandatory evaluations of the specifications on all vertices of the uncertain polytopic system in an explicit form. Instead, solving five LMIs exclusively suffices for ensuring the robust stability and performance regardless of the number of vertices, and thus, the typically heavy computational burden is considerably alleviated. It is also noteworthy that the proposed methodology additionally provides the necessary and sufficient conditions for this robust controller design with the consideration of a prescribed finite frequency range, and therefore, significantly less conservatism is attained in the system performance.