New results and examples on a class of discontinuous controllers

Robust stabilization of chained systems via hybrid control

“…On the other hand, many practical systems do not admit any smooth static or dynamic state stabilizer due to the violation of the well-known necessary condition [3]. To cope with this difficulty, many innovative nonsmooth control approaches have been proposed in recent years.…”

“…Most of the robust stabilization results and investigations focus on the problems of parametric uncertainties or model errors, see, e.g., [11] where the problem of local robust stabilization by means of time-varying control laws have been studied; [7], where a similar problem has been addressed using the class of discontinuous control laws introduced in, e.g., [1] and [6], where several types of hybrid control laws have been used to achieve local robustness against unknown parameters or unmodeled dynamics. On the other hand, the fundamental problems of robustness in the presence of sensor noise, external disturbances and actuator disturbances have been only partially addressed; see, e.g., [3] and [17].…”

“…On the contrary, the robust stabilization problem for nonholonomic systems is not yet completely solved. Several attempts have been made to study the robustness properties of existing control laws or to robustify given controllers [3], [7]. Most of the robust stabilization results and investigations focus on the problems of parametric uncertainties or model errors, see, e.g., [11] where the problem of local robust stabilization by means of time-varying control laws have been studied; [7], where a similar problem has been addressed using the class of discontinuous control laws introduced in, e.g., [1] and [6], where several types of hybrid control laws have been used to achieve local robustness against unknown parameters or unmodeled dynamics.…”