Robust H∞ control for fractional order singular systems 0 < α < 1 with uncertainty - Li, Bingxin; Zhao, Xin (Optimal control applications & methods, 2023)
This article studies robust H∞$$ H_{∞ } $$ control for fractional order singular systems (FOSS) 0<α<1$$ 0<α <1 $$ with uncertainty. First, the condition based on the linear matrix inequality (LMI) is obtained for fractional order systems with 0<α<1$$ 0<α <1 $$ in Corollary 1. Compared with existing results, by using two matrices to replace the complex matrix, the condition is easier to solve. Based on Corollary 1, the condition of H∞$$ H_{∞ } $$ control based on non‐strict LMI for FOSS without uncertainty is proposed. The strict LMI‐based conditions of H∞$$ H_{∞ } $$ control are improved to overcome the equality constraints. Finally, the LMI‐based conditions of robust H∞$$ H_{∞ } $$ control are proposed for FOSS. Four examples are shown to illustrate the effectiveness of the method.