This paper studies a class of impulsive switched systems with persistent bounded disturbance using robust attractor analysis and multiple Lyapunov functions. Some sufficient conditions for internal stability of the systems are obtained in terms of linear matrix inequalities (LMI). Based on the results, a simple approach for the design of a feedback controller is presented to achieve a desired level of disturbance attenuation. Numerical examples are also worked out to illustrate the obtained results.

In this work, the elementary task of controlling the contact of a one degree-of-freedom (dof) robot with a compliant surface is modeled as a switched system. A position controller is used for the free motion and a force controller for the contact task and the goal is to stabilize the robot in contact with the spring-like environment while exerting a desired force. As the robot makes or breaks contact, the control law switches accordingly and the aim is to examine the system's stability using ideas from hybrid stability theory. By considering typical candidate Lyapunov functions for each of the two discrete system states, conditions on feedback gains are derived that guarantee Lyapunov stability of the hybrid task. It is shown that conditions can be decoupled with respect to the discrete state only when the more general hybrid stability theorems are used.