Robust H∞ control for uncertain singular discrete T–S fuzzy time-delay systems with actuator saturation

Robust H∞ static output‐feedback control for discrete‐time fuzzy systems with actuator saturation via fuzzy Lyapunov functions

“…The LMI (34) in Theorem 2 is obtained from (37) via a Schur complement and using inequality (30). For verifying the inequality (b) in (36) the proof follows the same steps as for saturated control and is not repeated therein.…”

“…Motivated by the aforementioned observations, this paper intends to derive a robust H ∞ static output‐feedback control for discrete‐time fuzzy systems with cactuator saturation via FWDLF. The contributions of the proposed work are summarized as: (i)Unlike the fuzzy control design methods using a PDC controller for T‐S systems with actuator saturation, thus considering the state variables available; the presented SOF control work does not consider this strong assumption. (ii)Quadratic approaches' results , will be encapsulated into a FWDLF extended approach. (iii)The modeling errors and external perturbations are also taken into consideration via classical H ∞ attenuation using LMI constraints both for constrained and saturated control input. …”

“…Therefore, the control system design must take into account these input constraints in order not to degrade the performance of the closed-loop system that can even lead to instability issues [8,10,25,26,[30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45]. Many results are reported in the literature regarding stability analysis of linear (more recently, see [35][36][37][38]) and nonlinear systems [8,10,16,25,26,[31][32][33][34][40][41][42]45] subject to input constraints. Several approaches were experienced with T-S systems: bound on the initial conditions to avoid the input saturation in low gain control laws [16,26,40]; estimation of the attraction domain in the presence of actuator saturation [8,10,16,38,40,41,…”

“…(i) Unlike the fuzzy control design methods [32][33][34] using a PDC controller for T-S systems with actuator saturation, thus considering the state variables available; the presented SOF control work does not consider this strong assumption. (ii) Quadratic approaches' results [32][33][34]40,41], will be encapsulated into a FWDLF extended approach. (iii) The modeling errors and external perturbations are also taken into consideration via classical H ∞ attenuation using LMI constraints both for constrained and saturated control input.…”

T-S Fuzzy-Based Optimal Control for Minimally Invasive Robotic Surgery with Input Saturation

“…For this problem, [19,20] provided a finitetime control by optimal control and estimated the attraction domain. The combination of the T-S fuzzy model and optimal control show an animated controller design of a nonlinear system with actuator saturation [21]. For optimal control, Hu et al [22] provided a useful control method for the saturation system with actuator saturation based on a contractively invariant ellipsoid.…”