Robust $$H_{\infty }$$ H ∞ filtering for uncertain two-dimensional continuous systems with time-varying delays

Analysis and Design of $$H_{\infty }$$ H ∞ Controllers for 2D Singular Systems with Delays

“…12 We shall show that e(i, j) 2 < γ w(i, j) 2 under zero boundary conditions for any nonzero w(i, j) ∈ l 2 . For this, consider the following associated performance index:…”

“…Of these previous results, the H ∞ filtering problem for 2D linear systems has been studied in [2,7,8,[10][11][12]15,27,28,[30][31][32][33][34]41]; for 2D linear parameter-varying systems, the related work can be found in [9,32]; for 2D systems with delays, this filtering problem has been investigated in [27,31]; the stability and stabilization of 2D systems have been solved in [1,[17][18][19]26], while the H ∞ control for 2D nonlinear systems with delays and the nonfragile H ∞ and l 2 − l 1 problems were studied in [36]. Nonetheless, as no systematic and general approach to analyze 2D SRM systems exists, there are still many unsolved problems.…”

Necessary and Sufficient Stability Criterion and Stabilization for Positive 2‐D Continuous‐Time Systems with Multiple Delays

“…Recently, 2‐D continuous systems has also attained some attention and by utilizing the line integral technique, several valuable results about 2‐D continuous systems have been reported in . Lately, and studied and solved the robust H ∞ control and robust H ∞ filtering problems for 2‐D continuous systems with uncertainties and delays. Authors in , proposed the solution for the stability analysis and H ∞ control problems of switched 2‐D continuous systems.…”

Delay-dependent stability and stabilisation of continuous 2D delayed systems with saturating control

“…The 2D models, introduced in the 1970s (Fornasini & Marchesini, 1976;Givone & Roesser, 1972), have applications in, for example, data filtering, image processing (Roesser, 1975), and, in general, in systems described by partial differential equations, like the Darboux equation of processes like gas absorption, water stream heating, and air drying (see, e.g., Marszalek, 1984). In connection with Roesser (1975) and Fornasini and Marchesini (1976) models, many problems have been extensively investigated, such as realisation, controllability, minimum energy control, and H ∞ filtering (see, e.g., Boukili, Hmamed, Benzaouia, & El Hajjaji, 2014;El-Kasri, Hmamed, Alvarez, & Tadeo, 2012;El-Kasri, Hmamed, Tissir, & Tadeo, 2013;Hmamed, Alfidi, Benzaouia, & Tadeo, 2007;Kaczorek, 1997;Li & Gao, 2012). Nonetheless, the stabilisation problem is not fully solved for many classes of 2D systems.…”