Delay-range-dependent robust stabilization for uncertain T–S fuzzy control systems with interval time-varying delays

Stability analysis of delayed Takagi-Sugeno fuzzy systems: a new integral inequality approach

“…For comparisons, we study T-S fuzzy system (2.2) with fuzzy rules investigated in recent publications [1,2,10,12,13,20,21,25,27,32,33].…”

“…[18]). Consider the following time-delayed nonlinear system: x 1 (t) = 0.5(1 − sin 2 (θ(t)))x 2 (t) − x 1 (t − τ(t)) − (1 + sin 2 (θ(t)))x 1 (t), x 2 (t) = sgn(|θ(t)| − π 2 )(0.9cos 2 (θ(t)) − 1)x 1 (t − τ(t)) − x 2 (t − τ(t)) − (0.9 + 0.1cos 2 (θ(t)))x 2 (t), which can be exactly expressed as a T-S delayed system (2.2) with the following rules [18,20,21,25].…”

“…It is worth noting that in the case d 2 1.0, in the existing ones the delay are often limited as the unknown case, that is, the fast-varying delay case, while the present results can work as before when d 2 1.0. From Table 3, it can be seen that the proposed method yields less conservative that the exiting literatures [2,12,18,20,21,25,27]. Furthermore, to compare with the existing results in [10,12,13,21,32], we assume that h a = 0.…”

“…There have been many approaches in the literature based on various mathematical tools such as (improved) Jensen inequality [1-4, 7, 15, 17, 18, 21, 24, 25, 29, 32, 32], free-weighting matrix method [13,17,29], reciprocally convex approach [16,[31][32][33] and fuzzy-weightingdependent Lyapunov function method [7,28,31,34]. Recently, a delay partitioning approach has been proposed to further reduce their conservatism, see [1,2,7,11,14,18,20,31,32,34] and references therein. Yang et al [31] proposed an improved delay partitioning approach to stability analysis of delayed T-S fuzzy systems.…”

An approach to observer design of continuous-time Takagi–Sugeno fuzzy model with bounded disturbances

“…In fact, many fuzzy systems do not admit quadratic 8 Lyapunov function such as those discussed in [21], where a number of examples have been demonstrated and some similar expla-9 nations can also be found in [16]. Then, in order to reduce the conservativeness arisen from the using of single Lyapunov matrix, 10 various kinds of Lyapunov functions and important issues have been studied, such as time-delay model [37,39,42,43,53,54] and 11 network model [40] (others can be found in [15] and the references therein). One of these effective Lyapunov functions is the 12 non-quadratic Lyapunov function which was proposed in [17], further studied in [11] and now used widely in the fuzzy control.…”