Output feedback stabilization of uncertain dynamic systems with multiple state delays via sliding mode control strategy

This paper presents a design method of output feedback sliding mode control for stabilizing the uncertain systems with multiple state delays, when the system states are not available. The control scheme consists of two portions including the design of an approximating continuous control law and the determination of a special switching hyperplane. A special switching hyperplane is determined by employing the Bellman-Gronwall theorem, so that the system outputs are initially on the sliding hyperplane and sliding motion has a desired stable response. Furthermore, by means of the Lyapunov stability theorem, the authors derive an approximating continuous control law, which can not only guarantee the existence of the sliding mode but also avoid the chattering phenomenon. Then, the design procedure does not include solving the Lyapunov equation or Riccati equation. Finally, simulation results show the effectiveness of the proposed method.