Finite frequency H∞ control of singularly perturbed Euler-Lagrange systems: An artificial delay approach

In this paper, we show that small artificial delays in the feedback loops operating in different time scales may stabilize singularly perturbed systems (SPSs). An artificial delay approach is proposed for the robust stabilization and L-2-gain analysis of SPSs in the finite frequency domain. A two-time-scale delayed static output feedback controller is designed, in which the controller gains are formulated via a linear matrix inequality (LMI) algorithm. A distinctive feature of the proposed algorithm is setting controller parameters as free variables, which increases the degrees of freedom in controller design and leads to more flexibility in solving LMIs. Moreover, the proposed method is further extended to analyze the finite frequency system specifications of SPSs. The L-2-gain performance analysis is conducted for parameter-independent subsystems in their dominant frequency ranges, and the disturbance attenuation level of the original high-order system is then estimated. Finally, the efficiency of the proposed design method is verified in an active suspension system subject to multiple finite frequency disturbance.