Robust H<inf>&#x221E;</inf> filtering for uncertain 2-D continuous systems, based on a polynomially parameter-dependent Lyapunov function

H∞ Control for 2D Singular Continuous Systems

“…Theorem 6 is a simple application of Theorem 3 to the closed-loop system with A replaced by A + BK. A change in variable allows one to express the state feedback gain as in (26).…”

“…The problem of H ∞ performance analysis for 2D continuous time-varying delay systems has been addressed in [24]. The robust H ∞ filtering for uncertain 2D continuous systems based on a polynomial parameterdependent Lyapunov function has been studied in [26]. Furthermore, 2D singular systems have received great interest from the academic community due to their wide applications to describe physical systems in several practical areas [27,28].…”

C. El-Kasri, A. Hmamed, E. H. Tissir

“…In addition, certain 2-D systems containing digital processors that need finite numerical computation time [8], [28] display also the delay phenomenon. The stability and control problems of uncertain 2-D discrete state-delayed systems have been studies in [28], [29], whereas the H  filtering problem for 2-D continuous state-delayed systems (albeit with norm bounded uncertainties) was considered in [18].In this paper, motivated by the underlying idea in [25], we present a new approach, the structured polynomially parameter-dependent method, for designing the robust H  filters for uncertain 2D statedelayed systems described by the Roesser state-space model. Assuming parameter uncertainties in a polytope, the focus is on designing a filter such that the filtering error system is robustly asymptotically stable and the H  norm of the filtering error system for the entire uncertainty domain minimized.…”