Delay-Dependent Stabilizability of 2D Delayed Continuous Systems with Saturating Control

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

“…Thus, the results in Benhayoun et al (2013) can be seen as a special case. As the approach proposed here makes full use of slack matrices S andS, that dependent on the number of segments considered in the decomposition (N 1 and N 2 , respectively), in general, it will be less conservative than the one in Benhayoun et al (2013). For more details about this approach used, see, for example, Menga, Lam, Du, and Gao (2010) and Gao and Li (2011).…”

“…Remark 2: If the decomposition approach were not applied (i.e., when N 1 = N 2 = 1), the terms V 4 (x) and V 5 (x) of the LKF, V(x), can be added: in this case, V(x) is the same as the LKF in Benhayoun et al (2013). Thus, the results in Benhayoun et al (2013) can be seen as a special case.…”

“…It is clear that increasing the number of segments makes the computational problem more complex than the one proposed in Benhayoun et al (2013), although for low values of the number of segments the computational complexity is acceptable (for example, if N 1 = N 2 = 2, the number of variables is just 14).…”

“…In Benhayoun, Mesquine, and Benzaouia (2013), the stabilisation problem under saturation was studied and a solution proposed that uses a single Lyapunov-Krasovskii functional (LKF) for the boundary conditions. Instead, here a decomposition approach is proposed, based on dividing the boundary functionals x h 0 (θ, t 2 ) and x v 0 (t 1 , δ) into smaller segments, so that a different Lyapunov matrix can be used in each segment, to reduce the conservativeness.…”

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

“…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.…”