Robust stabilization of T–S fuzzy discrete systems with actuator saturation via PDC and non-PDC law

Finite-frequency model reduction of discrete-time T–S fuzzy state-delay systems

“…With the help of Definition 1, the finite-frequency model reduction problem can be formulated as follows: For a given stable T-S fuzzy state-delay system (4), frequency bounds ϑ 2 ≥ ϑ 1 , and a scalar γ > 0, find a stable reducedorder model (6) such that the approximation error system (7) satisfies a finitefrequency H ∞ performance (8).…”

“…Stability analysis and control synthesis of T-S fuzzy systems has been fully investigated by various methods: quadratic Lyapunov functions [2]- [6], piecewise Lyapunov functions [7], [8], fuzzy Lyapunov functions [9], homogenous polynomially parameter dependent Lyapunov functions [10]- [13], adaptive fuzzy approaches [14]- [16], and Type-2 fuzzy model [17]- [19], etc.…”

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

“…Especially, for discrete-time T-S fuzzy systems, results devoted to SOF control can be found in [5,12,18,19,21,23,24]; and especially, in [4] and [12], where a fuzzy weighting-dependent Lyapunov function (FWDLF) has been used. At last, some performances are generally to be added, H ∞ attenuation being one of the most widely used for T-S systems [8,[10][11][12][13]17,19,20,22,[25][26][27][28][29][30]. For real-time control, another important issue is the physical limitations of the actuators, such as input bounds and/or rate saturation constraints.…”

“…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,…”

“…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 [8,10,16,38,40,41,45]; transformation of the saturation into a dead-zone nonlinearity [8], use of a polytopic model to express the saturation constraints in [10,16,[20][21][22]25,26,[35][36][37][38][39][40][41]45].…”