Static Output Feedback Stabilization: Cascade Delayed Control Design for Chains of Integrators

In the paper, a delayed control for an even-order chain of integrators is proposed. It is known that for many differential models, in particular, for models of mechanical systems, the control problem is reduced to the stabilization of chain of integrators. The proposed method use a simple inductive design and cascade systems’ asymptotic stability property. For any order of the integrator the control is a linear combination of delayed state coordinates with odd indices, and it depends on three numerical parameters. The parameters are selected from the stability region of a second-order linear delayed system and they can vary within a wide range. The result obtained can be applied to the stabilization problem for systems with incomplete measurements. In particular, for some class of mechanical systems, the proposed control can be a derivative-free alternative of stabilizing control.