Robust Stability Analysis of Takagi–Sugeno Fuzzy Nonlinear Singular Systems with Time-Varying Delays Using Delay Decomposition Approach

Abstract

This paper investigates the problem of robust stability analysis for TakagiSugeno fuzzy nonlinear singular systems with time-varying delays. The nonlinear functions are assumed to satisfy the Lipschitz conditions. By constructing LyapunovKrasovskii functional with different weighted matrices, sufficient delay-dependent asymptotic stability conditions are expressed in terms of linear matrix inequalities. Further, delay decomposition approach is used to derive less conservative results. The effectiveness of the derived theoretical result is shown through numerical examples.

Observer‐based control of Takagi–Sugeno descriptor system with time‐varying delay: Free‐weighting matrix

“…In this article, we focus on the building of LKF as a simple way to obtain less conservative results. The proposed LKF differs from those used in References 3‐6,20,35 in that the nonintegral term $$$ {\eta}_1^T{\tilde{E}}^TP\tilde{E}{\eta}_1 $$$ has been augmented with $$$ {h}_1{\sigma}_1 $$$ and $$$ {h}_2{\sigma}_2 $$$ to activate the role of Wirtinger's inequality. Furthermore, we have introduced the cross‐terms $$$ {\sum}_{i=1}^2{\int}_{-{h}_i}^0{\int}_{t+\delta}^t{\left({f}_i(s)E\dot{x}(s)\right)}^T(s){U}_i\left({f}_i(s)E\dot{x}(s)\right) dsd\delta $$$ in the novel LKF where $$$ {f}_i(s) $$$ is a scalar function.…”

“…Thus, the free‐matrices technique has been applied to obtain less conservative results using the time‐derivative of the above cross‐terms. Note that, these cross‐terms are ignored in References 3‐6,20,35.…”

Adaptive sliding mode control for fuzzy singular systems with time delay and input nonlinearity

“…10,11 Based on the TS fuzzy model, there has been considerable research work appearing to address the control problem of nonlinear singular systems in the presence of time delays. [12][13][14][15][16][17] On a different research front, sliding mode control (SMC) is one of different robust control schemes used to cope with model uncertainties and nonlinearities by taking advantage of the concepts of sliding mode surface design and equivalent control. 18,19 Sliding mode control, considered as variable structure control, uses a discontinuous control to drive and then constrain the state trajectories to lie within a neighborhood of a specific switching surface on which the system meets the required control specifications.…”