Further Result on Passivity for Discrete-Time Stochastic T-S Fuzzy Systems with Time-Varying Delays

Abstract

The passivity for discrete-time stochastic T-S fuzzy systems with time-varying delays is investigated. By constructing appropriate Lyapunov-Krasovskii functionals and employing stochastic analysis method and matrix inequality technique, a delay-dependent criterion to ensure the passivity for the considered T-S fuzzy systems is established in terms of linear matrix inequalities (LMIs) that can be easily checked by using the standard numerical software. An example is given to show the effectiveness of the obtained result.

Robust H ∞ control for uncertain Markovian jump systems with mixed delays

“…By using Lemma 2, 𝛤 is equivalent to inequality (5), which means that ||𝑧|| 2 ≤ γ||𝑤|| 2 is satisfied for any nonzero 𝑤(t) ∈ L 2 [0, ∞), which ensures the asymptotical stability of system (4). Theorem 2 For a prescribed scalar γ > 0 and some given positive scalars τ m , τ M , u, h and matrix K, system (4) with condition ( 2) is robustly asymptotically stable and satisfies ‖𝑧(t)‖ 2 ≤ γ‖𝑤(t)‖ 2 for all nonzero 𝑤(t) ∈ L 2 [0, ∞) if there are matrices 𝑃 p > 0, 𝑄 i > 0 (i = 1, 2, 3), 𝑅 > 0, 𝑆 j > 0 ( j = 1, 2), and appropriate dimension matrices 𝑁 l , 𝑂 l (l = 1, 2, 3, 4, 5), and a scalar ε p > 0 such that the following LMI is satisfied:…”

“…[1][2][3][4] It is well recognized that the presence of time delay in a dynamical system is often a primary source of instability and performance degradation. Moreover, the delay-dependent [5] results are generally less conservative than the delay-independent ones, [6] especially when the delay is small. Recently, much attention has been paid to the robust stability problem for uncertain systems with time delays.…”

Hierarchical Rule-Base Reduction Fuzzy Control for Path Tracking Variable Linear Speed Differential Steer Vehicles

“…However, in most systems, such assumptions are not true. As such, there has been a great deal of work done showing both the passivity and robustness of time-delayed fuzzy systems [34], [35], [36].…”

Passivity analysis of impulsive coupled reaction-diffusion neural networks with and without time-varying delay

“…Thus, it is essential to consider the time-varying delay in impulsive CRDNNs. chaos control and synchronization and flow control [26][27][28][29][30][31][32][33]. The main point of passivity theory is that the passive properties of systems can keep the systems internally stable.…”