A descriptor-system approach for finite-frequency H∞ control of singularly perturbed systems

This paper investigates the robust control for a class of singularly perturbed systems in the presence of actuator saturation. The controller design problem is cast as a convex optimization formulation, and the descriptor-system approach and the finite-frequency control technique are used to alleviate the ill-conditioning of the systems and reduce the conservatism of control system specifications. A parameter-dependent Lyapunov function approach is used to study the stability of the closed-loop system, and time-domain constraints are then formulated to enhance the safe operation of the systems subject to actuator saturations. We characterize the disturbance attenuation capability from external disturbances to measurement outputs in concerned frequency ranges such that the numerical stiffness can be avoided by specifying the unknown matrices in the singularly perturbed form. The finite-frequency descriptor-system control method is applied to an armature-controlled DC motor system to verify its effectiveness and merits.