Global Stabilization of Uncertain SISO Dynamical Systems Using a Multiple Delayed Partial State Feedback Sliding Mode Control

This brief addresses the global stabilization of uncertain single input and single output (SISO) dynamical systems using sliding mode control with multiple delayed partial state feedback. It is shown that using only delayed partial state information, it is possible to stabilize a large class of SISO uncertain dynamical systems. Artificial stabilizing delay is introduced in the partial state feedback to make the reduced-order sliding mode dynamics of a given system asymptotically stable. It is demonstrated that despite the order of dynamical systems, using the information of just three states together with their delayed terms, can asymptotically stabilize the uncertain SISO dynamical system. A numerical example of a ball and wheel system is provided to demonstrate the efficacy of the proposed method.