T–S fuzzy-model-based robust stabilization for a class of nonlinear discrete-time networked control systems

Improved Stability and Stabilization Criteria for Uncertain T–S Fuzzy Systems with Interval Time-Varying Delay via Discrete Wirtinger-Based Inequality

“…One can see from Table 1 that the results provided by Theorem 1 à coincide with those obtained from [16], where Theorem 1 à denotes Theorem 1 with P 41 ¼ P 31 , P 42 ¼ P 32 , P 43 ¼ 0 and P 44 ¼ P 33 ; the results are obtained from Theorem 1 in this paper are better than those in [3,6,10,16,17,25] with relatively less demand of computation burden, and some improvements over [10] Table 2 gives the results of the two controller designs under the lower delay bound d 1 ¼ 1: one is based on the method given by [5], and the other is based on Theorem 3 of this paper. It can be seen from Table 2 that the results provided in this paper are less conservative than those by [5]. Moreover, to show the effectiveness of the obtained results, the membership function is assumed to be l 1 ¼ ð1 À 1=ð1 þ expðÀ6x 2 ðkÞ À 1:5pÞÞÞ Â ð1 þ 1=ð1þ expðÀ6x 2 ðkÞ À 1:5pÞÞÞ, l 2 ¼ 1 À l 1 , and let the scenario where the input delay changes randomly in the range 1 dðkÞ 10.…”

“…lemma 3 in [5]). Since the term X T 2 NX 2 is not ignored in the process of the proof, less-conservative results than those in [5] can be expected. This will be demonstrated later through numerical examples.…”

“…Moreover, if X 2 ¼ 0, lemma 2 will be simplified as the celebrated discrete Jensen inequality (i.e. lemma 3 in [5]). Since the term X T 2 NX 2 is not ignored in the process of the proof, less-conservative results than those in [5] can be expected.…”

“…From stability analysis and stabilization point of view, it is very important to find the allowable upper bound of the time delay, which allows the studied control systems to retain stable. Therefore, much effort has been made on stability analysis and stabilization of T-S fuzzy systems with/without time delays, see, for example [5,[20][21][22][23][24] and the references therein.…”

Control synthesis of Roesser type discrete-time 2-D T–S fuzzy systems via a multi-instant fuzzy state-feedback control scheme

“…By exploiting both the single Lyapunov function and the so-called parallel distributed compensation (PDC) control law [11], quadratic stabilization conditions for T-S fuzzy control systems have been addressed in the past two decades and many extensive results have been given in terms of LMIs, e.g., [12,13]. However, those existing quadratic stabilization conditions are very conservative and thus numerous slack variable methods have been proposed for further releasing its conservatism [14][15][16][17][18][19][20][21][22][23][24][25]. As far as the problem of control synthesis of discrete-time T-S fuzzy systems is concerned, the usage of both the nonquadratic Lyapunov function and the non-PDC control law has been fully investigated and several kinds of relaxed non-quadratic stabilization conditions have been proposed in the existing literature.…”