Robust Stability of Switched Interconnected Systems With Time-Varying Delays

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Huanbin Xue ◽  
Jiye Zhang ◽  
Hong Wang ◽  
Baoshan Jiang
Keyword(s):  
Exponential Stability ◽  
Lyapunov Functions ◽  
Nonlinear Dynamical Systems ◽  
Sufficient Conditions ◽  
Interconnected Systems ◽  
Time Varying ◽  
Differential Inequalities ◽  
Interconnected System ◽  
Robust Exponential Stability ◽  
Arbitrary Switching

The problem of robust exponential stability for a class of switched nonlinear dynamical systems with uncertainties and time-varying delays is investigated. On the assumption that each isolated subsystem of the interconnected system can be exponentially stabilized and the corresponding Lyapunov functions are available, using M-matrix property, the differential inequalities with time-varying delays are constructed. By the stability analysis of the differential inequalities, the sufficient conditions to ensure the robust exponential stability of the switched interconnected systems (SIS) under arbitrary switching are obtained. The proposed method, which neither requires the individual subsystems to share a common Lyapunov function (CLF), nor needs to know the values of individual Lyapunov functions at each switching time, would provide a new mentality for studying stability of arbitrary switching. In addition, by resorting to average dwell time approach, conditions for guaranteeing the robust exponential stability of SIS under constrained switching are derived. The proposed criteria are explicit, and they are convenient for practical applications. Finally, two numerical examples are given to illustrate the validity and correctness of the proposed theories.

DELAY-DEPENDENT ROBUST EXPONENTIAL STABILITY FOR UNCERTAIN RECURRENT NEURAL NETWORKS WITH TIME-VARYING DELAYS

2007 ◽  
Vol 17 (03) ◽  
pp. 207-218 ◽  
Author(s):  
BAOYONG ZHANG ◽  
SHENGYUAN XU ◽  
YONGMIN LI
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Robust Exponential Stability ◽  
Neuron Activation ◽  
Exponentially Stable

This paper considers the problem of robust exponential stability for a class of recurrent neural networks with time-varying delays and parameter uncertainties. The time delays are not necessarily differentiable and the uncertainties are assumed to be time-varying but norm-bounded. Sufficient conditions, which guarantee that the concerned uncertain delayed neural network is robustly, globally, exponentially stable for all admissible parameter uncertainties, are obtained under a weak assumption on the neuron activation functions. These conditions are dependent on the size of the time delay and expressed in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed stability results.

scholarly journals Robust Exponential Stability for LPD Discrete-Time System with Interval Time-Varying Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Kanit Mukdasai
Keyword(s):  
Exponential Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Discrete Time System ◽  
Time System ◽  
Robust Exponential Stability ◽  
Time Varying Delay ◽  
Varying Delay

This paper investigates the problem of robust exponential stability for uncertain linear-parameter dependent (LPD) discrete-time system with delay. The delay is of an interval type, which means that both lower and upper bounds for the time-varying delay are available. The uncertainty under consideration is norm-bounded uncertainty. Based on combination of the linear matrix inequality (LMI) technique and the use of suitable Lyapunov-Krasovskii functional, new sufficient conditions for the robust exponential stability are obtained in terms of LMI. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

Coordination Control for Multiagent Interconnected Systems

2011 ◽  
Author(s):  
Wassim M. Haddad ◽  
Sergey G. Nersesov
Keyword(s):  
Dynamical Systems ◽  
Lyapunov Functions ◽  
Nonlinear Dynamical Systems ◽  
Control Design ◽  
Interconnected Systems ◽  
Time Varying ◽  
Design Framework ◽  
Coordination Control ◽  
Nonlinear Dynamical ◽  
Stabilizing Controllers

This chapter describes a stability and control design framework for time-varying and time-invariant sets of nonlinear dynamical systems. The framework is applied to the problem of coordination control for multiagent interconnected systems predicated on vector Lyapunov functions. In multiagent systems, several Lyapunov functions arise naturally where each agent can be associated with a generalized energy function corresponding to a component of a vector Lyapunov function. The chapter characterizes a moving formation of vehicles as a time-varying set in the state space to develop a distributed control design framework for multivehicle coordinated motion control by designing stabilizing controllers for time-varying sets of nonlinear dynamical systems. The proposed cooperative control algorithms are shown to globally exponentially stabilize both moving and static formations.

scholarly journals New Robust Exponential Stability Criterion for Uncertain Neutral Systems with Discrete and Distributed Time-Varying Delays and Nonlinear Perturbations

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Sirada Pinjai ◽  
Kanit Mukdasai
Keyword(s):  
Exponential Stability ◽  
Model Transformation ◽  
Sufficient Conditions ◽  
Coefficient Matrix ◽  
Linear Matrix ◽  
Time Varying ◽  
Nonlinear Perturbations ◽  
Matrix Inequalities ◽  
Neutral Systems ◽  
Robust Exponential Stability

We investigate the problem of robust exponential stability for uncertain neutral systems with discrete and distributed time-varying delays and nonlinear perturbations. Based on the combination of descriptor model transformation, decomposition technique of coefficient matrix, and utilization of zero equation and new Lyapunov functional, sufficient conditions for robust exponential stability are obtained and formulated in terms of linear matrix inequalities (LMIs). The new stability conditions are less conservative and more general than some existing results.

scholarly journals Robust Exponential Stability of Impulsive Stochastic Neural Networks with Leakage Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Chunge Lu ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Lyapunov Functions ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Mean Square ◽  
Robust Exponential Stability ◽  
Time Varying Delay ◽  
The Stability ◽  
Varying Delay

This paper investigates mean-square robust exponential stability of the equilibrium point of stochastic neural networks with leakage time-varying delays and impulsive perturbations. By using Lyapunov functions and Razumikhin techniques, some easy-to-test criteria of the stability are derived. Two examples are provided to illustrate the efficiency of the results.

scholarly journals Observer-Based Robust Control Method for Switched Neutral Systems in the Presence of Interval Time-Varying Delays

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2473
Author(s):  
Hamid Ghadiri ◽  
Hamed Khodadadi ◽  
Saleh Mobayen ◽  
Jihad H. Asad ◽  
Thaned Rojsiraphisal ◽  
...  
Keyword(s):  
Exponential Stability ◽  
Control Method ◽  
Sufficient Conditions ◽  
Control Technique ◽  
Function Technique ◽  
Linear Matrix ◽  
Time Varying ◽  
Neutral Systems ◽  
Robust Exponential Stability ◽  
Switched Neutral Systems

In this study, the challenges of the controller design of a class of Uncertain Switched Neutral Systems (USNSs) in the presence of discrete, neutral, and time-varying delays are considered by using a robust observer-based control technique. The cases where the uncertainties are normbounded and time-varying are emphasized in this research. The adopted control approach reduces the prescribed level of disturbance input on the controlled output in the closed-loop form and the robust exponential stability of the control system. The challenge of parametric uncertainty in USNSs is solved by designing a robust output observer-based control and applying the Yakubovich lemma. Since the separation principle does not generally hold in this research, the controller and observer cannot be designed separately, sufficient conditions are suggested. These conditions are composed of applying the average dwell time approach and piecewise Lyapunov function technique in terms of linear matrix inequalities, which guarantees robust exponential stability of the observer-based output controller. Finally, two examples are given to determine the effectiveness of the proposed method.

Robust Exponential Stability of Large-Scale System With Mixed Input Delays and Impulsive Effect

2016 ◽  
Vol 11 (5) ◽  
Author(s):  
Huanbin Xue ◽  
Jiye Zhang ◽  
Weifan Zheng ◽  
Wang Hong
Keyword(s):  
Exponential Stability ◽  
Large Scale ◽  
Sufficient Conditions ◽  
Impulsive Effect ◽  
Differential Inequalities ◽  
Robust Exponential Stability ◽  
Large Scale System ◽  
Closed Loop Systems ◽  
The Stability ◽  
Input Delays

In this paper, a class of large-scale systems with impulsive effect, input disturbance, and both variable and unbounded delays were investigated. On the assumption that all subsystems of the large-scale system can be exponentially stabilized, and the stabilizing feedbacks and corresponding Lyapunov functions (LFs) for the closed-loop systems are available, using the idea of vector Lyapunov method and M-matrix property, the intero-differential inequalities with variable and unbounded delays were constructed. By the stability analysis of the intero-differential inequalities, the sufficient conditions to ensure the robust exponential stability of the large-scale system were obtained. Finally, the correctness and validity of the methods was verified by two numerical examples.

scholarly journals Hybrid Feedback Control for Exponential Stability and Robust H∞ Control of a Class of Uncertain Neural Network with Mixed Interval and Distributed Time-Varying Delays

Computation ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 62
Author(s):  
Charuwat Chantawat ◽  
Thongchai Botmart ◽  
Rattaporn Supama ◽  
Wajaree Weera ◽  
Sakda Noinang
Keyword(s):  
Neural Network ◽  
Feedback Control ◽  
Exponential Stability ◽  
Convex Combination ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Robust Exponential Stability ◽  
Attenuation Level ◽  
Delay Dependent

This paper is concerned the problem of robust H∞ control for uncertain neural networks with mixed time-varying delays comprising different interval and distributed time-varying delays via hybrid feedback control. The interval and distributed time-varying delays are not necessary to be differentiable. The main purpose of this research is to estimate robust exponential stability of uncertain neural network with H∞ performance attenuation level γ. The key features of the approach include the introduction of a new Lyapunov–Krasovskii functional (LKF) with triple integral terms, the employment of a tighter bounding technique, some slack matrices and newly introduced convex combination condition in the calculation, improved delay-dependent sufficient conditions for the robust H∞ control with exponential stability of the system are obtained in terms of linear matrix inequalities (LMIs). The results of this paper complement the previously known ones. Finally, a numerical example is presented to show the effectiveness of the proposed methods.

scholarly journals Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays

2011 ◽  
Vol 21 (4) ◽  
pp. 649-658 ◽  
Author(s):  
Qianhong Zhang ◽  
Lihui Yang ◽  
Daixi Liao
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Fuzzy Cellular Neural Networks ◽  
Inequality Technique

Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays Fuzzy cellular neural networks with time-varying delays are considered. Some sufficient conditions for the existence and exponential stability of periodic solutions are obtained by using the continuation theorem based on the coincidence degree and the differential inequality technique. The sufficient conditions are easy to use in pattern recognition and automatic control. Finally, an example is given to show the feasibility and effectiveness of our methods.

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