Robust Sliding Mode Boundary Stabilization for Uncertain Delay Reaction–Diffusion Systems

The robust exponential stabilization is addressed for uncertain delay reaction–diffusion systems via sliding mode boundary control (SMBC). First, a novel integral sliding mode surface (SMS) is proposed, on which system states slide to the equilibrium with an exponential convergence rate. Furthermore, the sliding mode boundary controller (SMBCr) is designed to steer system states to the SMS in finite time. A criterion is established for robust exponential stability by utilizing the Lyapunov–Krasovskii functional method and Wirtinger's inequality. Second, the boundary-output-based observer is constructed, and the observer-based SMBC is investigated. The observer states are required to reach the specified SMS in finite time. Then, a sufficient criterion is obtained that ensures the resultant system to realize robust exponential stability under the designed observer-based SMBCr. Finally, two examples of thermal conduction control of semiconductor power chips are proposed to illustrate the validity of theoretical results.