scholarly journals Reachable Set and Robust Mixed Performance of Uncertain Discrete Systems with Interval Time-Varying Delay and Linear Fractional Perturbations

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2763
Author(s):  
Chang-Hua Lien ◽  
Hao-Chin Chang ◽  
Ker-Wei Yu ◽  
Hung-Chi Li ◽  
Yi-You Hou
Keyword(s):  
Uncertain System ◽  
Discrete Systems ◽  
Reachable Set ◽  
Slow Variation ◽  
Time Varying ◽  
Interval Time ◽  
Time Varying Delay ◽  
The Stability ◽  
Varying Delay ◽  
Variation Interval

In this paper, the mixed performance and reachable set of uncertain discrete systems with slow variation interval time-varying delay are considered. The original uncertain discrete systems with interval time-varying delay are first transformed into a switched system. Then, the proposed improved results are used to guarantee the stability and reachable set of the uncertain system with slow variation interval time-varying delay. The mixed performance (H2/H∞) can be derived in the same formulation simultaneously. The design scheme of robust switched control is also developed in this paper. The gains of the controller can be designed and switched to achieve stabilization and mixed performance of the system according to the delay value. Some comparisons with published results are made to show the main contribution of the proposed approach. Finally, some numerical examples are illustrated to show the main results.

Delay-Dependent Criteria for Absolute Stability of Time-Varying Delay Lurie Control Systems

2015 ◽  
Vol 740 ◽  
pp. 234-237
Author(s):  
Wen Fang Xin ◽  
Shu Li Guo ◽  
Li Na Han
Keyword(s):  
Uncertain System ◽  
Time Varying ◽  
Problem Of Time ◽  
Time Varying Delay ◽  
Quadratic Trinomial ◽  
Q Matrix ◽  
The Stability ◽  
Delay Dependent ◽  
Nonlinear Uncertain System ◽  
Varying Delay

A new method for constructing a Lyapunov-Razumikhn function to deal with the stability problem of time-varying delay nonlinear uncertain system is presented in this paper. A quadratic trinomial with two variables（ξ,Τ）is obtained, and then the upper bound of the allowable delay Τ can be obtained by solving the optimization problem with varying positive matrix Q. That is to say, we can obtain the optimal combination of Τ and Q matrix.

scholarly journals A Delay Decomposition Approach to the Stability Analysis of Singular Systems with Interval Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Jianmin Jiao ◽  
Rui Zhang
Keyword(s):  
Singular Systems ◽  
Time Varying ◽  
Decomposition Approach ◽  
Interval Time ◽  
Time Varying Delay ◽  
Delay Decomposition Approach ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper investigates delay-dependent stability problem for singular systems with interval time-varying delay. An appropriate Lyapunov-Krasovskii functional is constructed by decomposing the delay interval into multiple equidistant subintervals, where both the information of every subinterval and time-varying delay have been taken into account. Employing the Lyapunov-Krasovskii functional, improved delay-dependent stability criteria for the considered systems to be regular, impulse-free, and stable are established. Finally, two numerical examples are presented to show the effectiveness and less conservativeness of the proposed method.

New Delay-Dependent Approach on Stability for Systems with Interval Time-Varying Delay

2011 ◽  
Vol 181-182 ◽  
pp. 325-329
Author(s):  
Tao Zhang ◽  
Yan Qiu Cui ◽  
Juan Wang ◽  
Jin Sheng Sun
Keyword(s):  
Model Transformation ◽  
Time Varying ◽  
Stability Criteria ◽  
Theoretical Derivation ◽  
Interval Time ◽  
Time Varying Delay ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

In this paper, the stability of systems with interval time-varying delay is investigated. The time delay varies in an interval. By employing a new and tighter integral inequality and constructing an appropriate type of Lyapunov functional, the delay-dependent stability criteria are derived. Because neither any model transformation nor free weighting matrices are employed in the theoretical derivation, the developed stability criteria significantly improve and simplify the existing stability conditions.

Robust Absolute Stability Criteria for Uncertain Lurie System With Interval Time-Varying Delay

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Pankaj Mukhija ◽  
Indra Narayan Kar ◽  
Rajendra K. P. Bhatt
Keyword(s):  
Absolute Stability ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Interval Time ◽  
Time Varying Delay ◽  
Wirtinger Inequality ◽  
Chua’S Oscillator ◽  
The Stability ◽  
Varying Delay

This paper addresses the problem of absolute stability of Lurie system with interval time-varying delay. The delay range is divided into two equal segments and an appropriate Lyapunov–Krasovskii functional (LKF) is defined. A tighter bounding technique for the derivative of LKF is developed. This bounding technique in combination with the Wirtinger inequality is used to develop the absolute stability criterion in terms of linear matrix inequalities (LMIs). The stability analysis is also extended to the Lurie system with norm-bounded parametric uncertainties. The effectiveness of the proposed approach has been illustrated through a numerical example and Chua's oscillator.

A new control approach for a class of linear switched systems with time-varying delay

2021 ◽  
pp. 014233122199272
Author(s):  
Abbas Zabihi Zonouz ◽  
Mohammad Ali Badamchizadeh ◽  
Amir Rikhtehgar Ghiasi
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Switching Systems ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Linear Switching Systems ◽  
The Stability ◽  
Varying Delay

In this paper, a new method for designing controller for linear switching systems with varying delay is presented concerning the Hurwitz-Convex combination. For stability analysis the Lyapunov-Krasovskii function is used. The stability analysis results are given based on the linear matrix inequalities (LMIs), and it is possible to obtain upper delay bound that guarantees the stability of system by solving the linear matrix inequalities. Compared with the other methods, the proposed controller can be used to get a less conservative criterion and ensures the stability of linear switching systems with time-varying delay in which delay has way larger upper bound in comparison with the delay bounds that are considered in other methods. Numerical examples are given to demonstrate the effectiveness of proposed method.

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

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
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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