Exponential Stability and H∞$$ {H}_{\infty } $$ Controller Design for 2‐D Discrete‐State Systems in Roesser Model With Directional Delays

Abstract

This study looks at the problems related to exponential stability and controller design for a specific class of two‐dimensional discrete‐state systems (2‐D‐DSS) with directional constant delays (DCDs) in the Roesser model. Initially, by applying the two‐dimensional (2‐D) Lyapunov–Kravoskii functional approach, a condition is formulated as a linear matrix inequality (LMI) to ensure that the system remains exponentially stable while achieving an performance level of . Following this, a approach for designing a state feedback controller (SFB‐) is presented as a practical application of the derived results. Finally, several examples are provided to demonstrate the effectiveness of the proposed results.