Discontinuous control systems in the presence of measurement noise

In this paper the properties of a class of piecewise continuous systems subject to measurement noise are studied especially regarding their possibility to be stabilized around a whatever vector whitin a finite set of desired stabilization points. Such a problem is a typical control issue in many real systems (vehicles attitude control, robotic manipulators, etc.). Conditions under which global asymptotic stability to a set of points can be guaranteed have been studied in the past by exploiting the intrinsic “holding” nature of the discrete-time control framework, which can be emulated in continuous-time by the introduction of sample-and-hold strategies. Because such conditions can be conservative in some cases, new policies are here introduced and investigated based on the notion of “strategy holding” in time (by providing a slower switching policy sampling time) and space (by using hysteresis regions).