Robustness of discontinuous feedback in control under disturbance∗ Dedicated to Jack Warga on occasion of his 80th birthday

It is well known that various control tasks ( optimization of cost functionals, stabilization and etc.) cannot be performed by using continuous feedbacks. But an application of discontinuous feedback immediately poses a question of its robustness with respect to external disturbances, actuator and measurement errors. In this paper we discuss a concept of discontinuous feedback for control systems under persistent disturbances which is robust with respect to all above mentioned disturbances and errors. These discontinuous feedbacks are robust not only with respect to errors and disturbances of small amplitude and infinite impulse but also with respect to actuator errors and external disturbances of infinite amplitude and small impulse.