Robust Fault Estimation for a Class of T-S Fuzzy Singular Systems with Time-Varying Delay via Improved Delay Partitioning Approach

The problem of delay-dependent robust fault estimation for a class of Takagi-Sugeno (T-S) fuzzy singular systems is investigated. By decomposing the delay interval into two unequal subintervals and with a new and tighter integral inequality transformation, an improved delay-dependent stability criterion is given in terms of linear matrix inequalities (LMIs) to guarantee that the fuzzy singular system with time-varying delay is regular, impulse-free, and stable firstly. Then, based on this criterion, by considering the system fault as an auxiliary disturbance vector and constructing an appropriate fuzzy augmented system, a fault estimation observer is designed to ensure that the error dynamic system is regular, impulse-free, and robustly stable with a prescribedH∞performance satisfied for all actuator and sensor faults simultaneously, and the obtained fault estimates can practically better depict the size and shape of the faults. Finally, numerical examples are given to show the effectiveness of the proposed approach.

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Improved Results on Stability Criteria for Singular Systems with Interval Time-Varying Delays

Journal of Circuits System and Computers ◽

10.1142/s0218126621300014 ◽

2020 ◽

pp. 2130001

Author(s):

Chaibi Noreddine ◽

Belamfedel Alaoui Sadek ◽

Tissir El Houssaine ◽

Bensalem Boukili

Keyword(s):

Singular Systems ◽

Singular System ◽

Delay Systems ◽

Linear Matrix ◽

Time Varying ◽

Time Varying Delay ◽

Small Gain ◽

The Stability ◽

Varying Delay ◽

Singular Time

The purpose of this paper is to address the problem of assessing the stability of singular time-varying delay systems. In order to highlight the relations between the delay and the state, the singular system is transformed into a neutral form. Then, a model transformation using a three-terms approximation of the delayed state is exploited. Based on the lifting method and the Lyapunov–Krasovskii functional (LKF) method, a new linear matrix inequality (LMI) is obtained, allowing conclusions on stability to be drawn using the scaled small gain theorem (SSG). The use of SSG theorem for stability of singular systems with time-varying delay has not been investigated elsewhere in the literature. This represents the main novelty of this article. The result is applicable for assessing the stability of both singular systems and neutral systems with time-varying delays. The less conservativeness of the stability test is illustrated by comparison with recent literature results.

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Delay-Range-Dependent Stability Criteria for Takagi-Sugeno Fuzzy Systems with Fast Time-Varying Delays

Journal of Applied Mathematics ◽

10.1155/2012/475728 ◽

2012 ◽

Vol 2012 ◽

pp. 1-20 ◽

Cited By ~ 2

Author(s):

Pin-Lin Liu

Keyword(s):

Linear Matrix ◽

Fast Time ◽

Time Varying ◽

Stability Criteria ◽

Decomposition Approach ◽

Time Varying Delay ◽

Delay Decomposition Approach ◽

Delay Dependent ◽

Takagi Sugeno ◽

Varying Delay

The problem of delay-range-dependent stability for T-S fuzzy system with interval time-varying delay is investigated. The constraint on the derivative of the time-varying delay is not required, which allows the time delay to be a fast time-varying function. By developing delay decomposition approach, integral inequalities approach (IIA), and Leibniz-Newton formula, the information of the delayed plant states can be taken into full consideration, and new delay-dependent sufficient stability criteria are obtained in terms of linear matrix inequalities (LMIs) which can be easily solved by various optimization algorithms. Simulation examples show resulting criteria outperform all existing ones in the literature. It is worth pointing out that our criteria are carried out more efficiently for computation and less conservatism of the proposed criteria.

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Delay-Dependent Stability Criteria for Singular Systems with Interval Time-Varying Delay

Mathematical Problems in Engineering ◽

10.1155/2012/570834 ◽

2012 ◽

Vol 2012 ◽

pp. 1-16 ◽

Cited By ~ 7

Author(s):

Jianmin Jiao

Keyword(s):

Singular Systems ◽

Linear Matrix ◽

Time Varying ◽

Stability Criteria ◽

Interval Time ◽

Time Varying Delay ◽

Decision Variables ◽

Delay Dependent ◽

Delay Dependent Stability ◽

Varying Delay

This paper is concerned with stability analysis for singular systems with interval time-varying delay. By constructing a novel Lyapunov functional combined with reciprocally convex approach and linear matrix inequality (LMI) technique, improved delay-dependent stability criteria for the considered systems to be regular, impulse free, and stable are established. The developed results have advantages over some previous ones as they involve fewer decision variables yet less conservatism. Numerical examples are provided to demonstrate the effectiveness of the proposed stability results.

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Dissipative Filter Design for Nonlinear Time-Varying-Delay Singular Systems against Deception Attacks

Complexity ◽

10.1155/2021/2260753 ◽

2021 ◽

Vol 2021 ◽

pp. 1-15

Author(s):

Guobao Liu ◽

Shibin Shen ◽

Xianglei Jia

Keyword(s):

Filter Design ◽

Singular Systems ◽

Signal Transmission ◽

Fuzzy Model ◽

Linear Matrix ◽

Time Varying ◽

Time Varying Delay ◽

Measurement Output ◽

Delay Dependent ◽

Varying Delay

This paper applies a T-S fuzzy model to depict a class of nonlinear time-varying-delay singular systems and investigates the dissipative filtering problem for these systems under deception attacks. The measurement output is assumed to encounter random deception attacks during signal transmission, and a Bernoulli distribution is used to describe this random phenomena. In this case, the filtering error system modeled by a stochastic singular T-S fuzzy system is established and stochastic admissibility for this kind of system is defined firstly. Then, by combining some integral inequalities and using the Lyapunov–Krasovskii functional approach, sufficient delay-dependent conditions are presented based on linear matrix inequality techniques, where the system of filtering error can be stochastically admissible and strictly ℚ , S , ℝ -dissipative against randomly occurring deception attacks. Moreover, parameters of the desired filter can be obtained via the solutions of the established conditions. The validity of our work is illustrated through a mostly used example of the nonlinear system.

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Novel Stabilization Conditions for Uncertain Singular Systems with Time-Varying Delay

Mathematical Problems in Engineering ◽

10.1155/2014/796596 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8

Author(s):

Yuanchun Ding ◽

Falu Weng ◽

Ji Ge ◽

Qi Liang ◽

Xueyi Zhi

Keyword(s):

Singular Systems ◽

Singular System ◽

Robust Stabilization ◽

State Feedback Control ◽

Delay Systems ◽

Time Varying ◽

Time Varying Delay ◽

Uncertain Singular Systems ◽

Delay Dependent ◽

Varying Delay

The problem of delay-dependent robust stabilization for continuously singular time-varying delay systems with norm-bounded uncertainties is investigated in this paper. First, based on some mathematical transform, the uncertain singular system is described in a form which involves the time-delay integral items. Then, in terms of the delay-range-dependent Lyapunov functional and the LMI technique, the improved delay-dependent LMIs-based conditions are established for the uncertain singular systems with time-varying delay to be regular, causal, and stable. Furthermore, by solving these LMIs, an explicit expression for the desired state feedback control law can be obtained; thus, the regularity, causality, and stability of the closed-loop system are guaranteed. In the end, numerical examples are given to illustrate the effectiveness of the proposed methods.

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Improved Stability Criteria of Static Recurrent Neural Networks with a Time-Varying Delay

The Scientific World JOURNAL ◽

10.1155/2014/391282 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7 ◽

Cited By ~ 2

Author(s):

Lei Ding ◽

Hong-Bing Zeng ◽

Wei Wang ◽

Fei Yu

Keyword(s):

Neural Networks ◽

Recurrent Neural Networks ◽

Linear Matrix ◽

Time Varying ◽

Time Varying Delay ◽

Improved Stability ◽

The Stability ◽

Delay Dependent ◽

Delay Dependent Stability ◽

Varying Delay

This paper investigates the stability of static recurrent neural networks (SRNNs) with a time-varying delay. Based on the complete delay-decomposing approach and quadratic separation framework, a novel Lyapunov-Krasovskii functional is constructed. By employing a reciprocally convex technique to consider the relationship between the time-varying delay and its varying interval, some improved delay-dependent stability conditions are presented in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the merits and the effectiveness of the proposed methods.

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Convex Polyhedron Method to Stability of Continuous Systems with Two Additive Time-Varying Delay Components

Journal of Applied Mathematics ◽

10.1155/2012/689820 ◽

2012 ◽

Vol 2012 ◽

pp. 1-13 ◽

Cited By ~ 1

Author(s):

Tiejun Li ◽

Junkang Tian

Keyword(s):

Stability Criterion ◽

Convex Polyhedron ◽

Linear Matrix ◽

Continuous Systems ◽

Time Varying ◽

Time Varying Delay ◽

Polyhedron Method ◽

Delay Dependent ◽

Delay Dependent Stability ◽

Varying Delay

This paper is concerned with delay-dependent stability for continuous systems with two additive time-varying delay components. By constructing a new class of Lyapunov functional and using a new convex polyhedron method, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities. The obtained stability criterion is less conservative than some existing ones. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.

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New Delay-Dependent Robust Stability Criterion for Uncertain Stochastic Systems with Time-Varying Delays

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.461.633 ◽

2012 ◽

Vol 461 ◽

pp. 633-636

Author(s):

Cheng Wang

Keyword(s):

Robust Stability ◽

Stability Criterion ◽

Stochastic Systems ◽

Linear Matrix ◽

Time Varying ◽

Time Varying Delay ◽

Weighting Matrix ◽

Delay Dependent ◽

Delay Dependent Stability ◽

Varying Delay

The problem of delay-dependent robust stability of uncertain stochastic systems with time-varying delay is discussed in this paper. Based on the Lyapunov-Krasovskii theory and free-weighting matrix technique, new delay-dependent stability criterion is presented. The criterion is in terms of linear matrix inequality (LMI) which can be solved by various available algorithms.

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