New perspective on sampled-data control for persistent dwell-time switched PDE systems with 2D spatial diffusion

Existing research has rarely focused on sampled-data control for switched partial differential equation (PDE) systems with two-dimensional (2D) spatial diffusion and a persistent dwell-time (PDT) switching rule, despite their strong application background in science and engineering. Therefore, a novel sampled-data control scheme for a class of switched PDE systems in 2D space is proposed in this paper. First, to accurately describe the fast and slow switching phenomena of the systems, PDT switching rule is used to model target switched PDE systems. The main advantage of PDT switching rule is being able to overcome the strict switching frequency limitations of dwell-time and average dwell-time switching rules. Moreover, a 2D spatial sampled-data control strategy, where the system’s continuous state $z(t,x_1,x_2)$ is sampled as discrete states $z(t_k,x_{1,\tilde{m}},l_2)$ and $z(t_k,l_1,x_{2,\hat{m}})$, is employed to achieve system stabilization. This ensures system stability while reducing control costs compared to distributed control. Then, to address the asynchronous difficulties caused by switching and sampling when analyzing the systems’ stability, iteration, recursion, and equiprobable summation are used and sufficient conditions are obtained to ensure the closed-loop system’s stability. Finally, the effectiveness of the proposed method is verified through two simulations.