A two-valued state feedback control for a second order plant with low switching rate

In this work a two-valued state feedback control is developed for a plant of second order with known constant coefficients and no disturbance, and for a plant with unknown varying coefficients and additive disturbance with known upper and lower bounds. A reference model is used in order to avoid large commutation rate of the control input. In the first part of the present work, the controller is developed by means of the Lyapunov-like function method achieving the convergence of the tracking error to a residual set whose size is user-defined. In the second part, the Lyapunov function at zero time is inside a predefined set and the developed controller forces the Lyapunov function to dwell inside such set. The size of this set is chosen such that the tracking error asymptotically converges to a residual set of user-defined size.

► We develop a two-valued state feedback control for a second order plant.
► The design guarantees convergences to a pre-established region defined by the user.
► The tracking error converges to a residual set defined by the user.
► The design includes uncertainties in the parameters and additive disturbance.
► With this design we obtain low commutation rate.