Finite-time H ∞ control for singularly perturbed systems subject to finite-frequency specification

Abstract

This paper investigates the design of a parameter-independent finite-time H∞ controller for singularly perturbed systems to address numerical ill-conditioning and enhance robustness under finite-frequency specifications. By integrating the descriptor-system approach with the generalised Kalman–Yakubovic˘–Popov lemma, the controller synthesis problem is formulated as a convex multi-objective optimisation problem. First, sufficient stability conditions under prescribed performance constraints are established using parameter-dependent Lyapunov functions. Subsequently, a less conservative finite-frequency bounded realness property is introduced to characterise the system's disturbance attenuation capability. By defining unknown variables in a parameter-dependent form, the numerical stiffness inherent in the equivalent linear matrix inequalities is effectively mitigated. The proposed method applies to both standard and nonstandard singularly perturbed systems. Finally, the validity of the proposed controller design method is demonstrated by an example.