H221E; Switched Controller Design for a Class of Uncertain Linear Systems Using Derivative Feedback

This manuscript proposes ${\mathcal {H}}_{\infty }$ switched controller designs for a class of linear systems with time-invariant uncertainties, where only the derivative of the state vector is used for feedback. We propose two strategies using auxiliary dynamics, which have accessible state vectors for feedback, to control the original plant. The first strategy uses a static feedback-gain matrix, while the second uses a set of feedback-gain matrices, selecting one of them through a switching law each time for feedback. Both designs ensure stability, decay rate constraints, and an ${\mathcal {H}}_{\infty }$ guaranteed cost for the original plant. Theoretical analyses and numerical examples demonstrate that the switched control law is superior to a constant feedback gain and a derivative feedback controller previously proposed in the literature for uncertain linear systems. We provide simulation examples that show the effectiveness of the proposed approach. In these examples, the proposed approach presents better results than another method in the literature when the external disturbance is zero ( $w(t)=0$ ). We also report a practical implementation of the designed switched controller in a Quanser® active suspension system. This case study, where the system is subject to uncertain parameters and actuator faults, highlights the method’s effectiveness.