Suboptimal robust linear visual servoing for a delayed underactuated system

In this contribution, a suboptimal robust control law for a specific class of underactuated delayed system is synthesized. The control strategy based on very well-known results for delay-dependent stability considers the time delay involved in the dynamical system, which affects to control signal. This contribution illustrates how the theoretical results can be used to improve the real-time performance of the closed-loop system considered. The delay is introduced into the control system by the vision module, due to the time required to perform the image treatment. In order to show the good performance of the control law proposed, real-time experiments are developed by applying a visual servoing technique on the cart-inverted pendulum system. Obtained results also illustrate how the conservativeness of theoretical results affects the performance of the closed-loop system and the negative effects of delays in the control loop. Furthermore, a robust stability analysis is done to establish the robustness of control law with respect to the amount of delay presented in the system.Copyright 2012 John Wiley & Sons, Ltd.