A new output regulation using sliding-mode technique for a class of SISO linear time-varying systems

In this brief, we propose a new output regulator using the sliding-mode technique for a class of single-input single-output linear time-varying (LTV) systems. It is seen that a bounded D-similarity-transformation matrix is first designed, which is necessary for the transformed LTV system to retain the dynamical features of the original LTV system. The update law of the transformation matrix based on the eigenstructure-assignment technique is developed to guarantee the uniformly exponential convergence of the closed-loop dynamics on the sliding mode. A sliding-mode output regulator using only the output measurements is then designed to drive both the sliding variable and the system output to converge to zero in a finite time. A simulation example is given in support of the proposed scheme.