Composite anti-disturbance impulsive control for a class of nonlinear systems via disturbance observers

Abstract

This paper studies an anti-disturbance impulsive control problem for a class of nonlinear systems with sampled measurements and input disturbances. It considers that the unknown input disturbances are generated by an exogenous system with additional disturbances. The goal is to construct an impulsive disturbance observer (IDO) to estimate the external disturbance and to use the disturbance estimate as a feed-forward compensator of the impulsive control so that the input disturbance can be rejected. Two types of design schemes are proposed in the linear matrix inequality framework. For the plants with sampled output measurements, a full-order IDO is constructed, under which both the state and the external disturbance can be estimated simultaneously. For the plants with state information available at impulse instants, a reduced-order IDO is designed, where only the estimation of the external disturbance is involved. Accordingly, the $H_{\infty }$ performance levels relative to the capability against the additional disturbance are respectively analyzed. Finally, an illustrative example is presented to demonstrate the validity of the results.