Control Design for Linear Systems with Commensurate Delays Via Coordinate Transformation: A Single-Input Case Study

The design of control for systems with commensurate delays with single input is proposed. The key to the design is to find a similarity transformation such that, in the new coordinates, all delays are aligned in the same input channel. A necessary and sufficient condition is established for transforming the system into the desired controllable form. Moreover, our analysis demonstrates that incorporation of a stable asymptotic observer in the state feedback does not impair stability of the system.