H∞ control of fractional-order singularly perturbed systems: The 1 < ν < 2 case

This paper addresses the problems of the H
∞
analysis and control of fractional-order singularly perturbed systems with the commensurate order 1 < ν < 2. Based on the bounded real lemma for fractional-order systems and singular fractional-order systems, the sufficient conditions for the H
∞
performance analysis of fractional-order singularly perturbed systems are firstly presented in terms of -independent linear matrix inequalities (LMIs). Then, the state feedback controllers are designed, and the sufficient -independent stabilization conditions are established via bilinear matrix inequalities(BMIs). Moreover, by the provided iterative algorithm, these BMI-based conditions can be solved based on LMIs. Finally, two numerical examples are exploited to verify the effectiveness of the proposed results.