Delay-dependent robustH_∞control for uncertain stochastic T–S fuzzy systems with time-varying state and input delays

Non-quadratic local stabilization for continuous-time Takagi–Sugeno models

“…hold for a given q ≥ 3 with i jl = block-diag[ i jl , i j ], (12), then x(t) tends to zero exponentially for any trajectory satisfying (6) …”

“…This method usually leads to conditions formulated in terms of linear matrix inequalities (LMIs) [4], which can be efficiently solved by convex optimization techniques. Quadratic analysis and design has produced a remarkable number of results regarding robustness, performance, observer design, output feedback and time delay systems (see e.g., [5][6][7][8][9] and references therein). Nonetheless, the quadratic approach presents serious limitations because its solutions are inherently pessimistic, i.e., there are stable or stabilizable models which do not have a quadratic solution (see [10] and references therein).…”

Robust control for T–S fuzzy systems with probabilistic interval time varying delay

“…By Lemma 1, we can arrive at conclusion that (15) and (16) imply the right hand side of (25) is less than zero. Therefore, there exists a scalar λ > 0 such that…”

“…Since then, many researchers have devoted much effort to both theoretical research and practical applications for various T-S fuzzy systems with time delays. Generally speaking, the published results on the stability analysis and design of nonlinear time-delay systems can be classified into two categories: delay-independent, e.g., [11] and delay-dependent, e.g., [12][13][14][15] and the references therein. In general, the delay-dependent criteria are less conservative than the delay-independent ones when the size of time delay is small.…”

Delay-dependent Robust Stabilization and H∞ Control for Uncertain Stochastic T-S Fuzzy Systems with Discrete Interval and Distributed Time-varying Delays

“…Recently, some attempts have Manuscript received March 15, 2011; revised March 31, 2012 been made to use T-S fuzzy model based control technique for stochastic nonlinear systems [27−30] . Very recently, the delay-dependent robust H∞ control for uncertain stochastic T-S fuzzy systems with time delays have been discussed in [31,32]. However, to the best of our knowledge, the delaydependent robust stabilization and H∞ control for uncertain stochastic T-S fuzzy systems with discrete interval and distributed time-varying delays have not yet been fully investigated and this will be the goal of this paper.…”