scholarly journals Full-Order Disturbance-Observer-Based Control for Singular Hybrid System

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Xiuming Yao ◽  
Ze Dong ◽  
Dongfeng Wang
Keyword(s):  
Lyapunov Stability ◽  
Hybrid System ◽  
Disturbance Observer ◽  
Composite System ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Control Scheme ◽  
System States

The problem of the disturbance-observer-based control for singular hybrid system with two types of disturbances is addressed in this paper. Under the assumption that the system states are, unavailable, full-order observers (for both system states and the disturbance) and a nonlinear control scheme are constructed, such that the composite system can be guaranteed to be stochastically admissible, and the two types of disturbances can be attenuated and rejected, simultaneously. Based on the Lyapunov stability theory, sufficient conditions for the existence of the desired full-order disturbance-observer-based controllers are established in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the effectiveness of the proposed approaches.

scholarly journals Sufficient Conditions on the Exponential Stability of Neutral Stochastic Differential Equations with Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Yanwei Tian ◽  
Baofeng Chen
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Stochastic Differential Equations ◽  
Lyapunov Stability ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Delay Dependent

The exponential stability is investigated for neutral stochastic differential equations with time-varying delays. Based on the Lyapunov stability theory and linear matrix inequalities (LMIs) technique, some delay-dependent criteria are established to guarantee the exponential stability in almost sure sense. Finally a numerical example is provided to illustrate the feasibility of the result.

scholarly journals LMI-Based Stability Criteria for Discrete-Time Neural Networks with Multiple Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Hui Xu ◽  
Ranchao Wu
Keyword(s):  
Neural Networks ◽  
Continuous Time ◽  
Discrete Model ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Multiple Delays ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Neural Models

Discrete neural models are of great importance in numerical simulations and practical implementations. In the current paper, a discrete model of continuous-time neural networks with variable and distributed delays is investigated. By Lyapunov stability theory and techniques such as linear matrix inequalities, sufficient conditions guaranteeing the existence and global exponential stability of the unique equilibrium point are obtained. Introduction of LMIs enables one to take into consideration the sign of connection weights. To show the effectiveness of the method, an illustrative example, along with numerical simulation, is presented.

scholarly journals Passivity analysis of multiple time-varying time delayed complex variable neural networks in finite-time

2021 ◽  
Vol 8 (4) ◽  
pp. 842-854
Author(s):  
N. Jayanthi ◽  
◽  
R. Santhakumari ◽  
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Multiple Time ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Complex Valued ◽  
Theoretical Results

In this article, we investigate the problem of finite-time passivity for the complex-valued neural networks (CVNNs) with multiple time-varying delays. To begin, many definitions relevant to the finite-time passivity of CVNNs are provided; then the suitable control inputs are designed to guarantee the class of CVNNs are finite-time passive. In the meantime, some sufficient conditions of linear matrix inequalities (LMIs) are derived by using inequalities techniques and Lyapunov stability theory. Finally, a numerical example is presented to illustrate the usefulness of the theoretical results.

Resilient anti-disturbance H∞ control for turbofan systems

2020 ◽  
Vol 42 (14) ◽  
pp. 2686-2697
Author(s):  
Yankai Li ◽  
Mou Chen ◽  
Tao Li ◽  
Huijiao Wang ◽  
Yu Kang
Keyword(s):  
Disturbance Observer ◽  
Closed Loop ◽  
Control Method ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Control Technique ◽  
Linear Matrix ◽  
Asymptotically Stable ◽  
Matrix Inequality ◽  
Closed Loop Systems

The problem of [Formula: see text] control is investigated for turbofan systems with uncertain parameters and multiple disturbances in this paper. Some disturbances with partly known information are described via an external system, and other disturbances are assumed to be [Formula: see text] norm bounded. According to the disturbance-observer-based-control (DOBC) method and resilient [Formula: see text] control technique, a robust resilient controller is designed to reject and attenuate the influence of these disturbances, and guarantees that closed-loop systems are asymptotically stable with [Formula: see text] performance. Some solvable sufficient conditions are obtained based on the linear matrix inequality (LMI) technique and Lyapunov stability theory. Finally, a simulation is presented to show the robustness and effectiveness of the developed resilient anti-disturbance [Formula: see text] control method.

scholarly journals H∞ Control for LPV Discrete Systems with Random Time-Varying Network Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Kewang Huang ◽  
Tao Ma ◽  
Feng Pan
Keyword(s):  
Linear Matrix Inequalities ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Discrete Systems ◽  
Performance Criterion ◽  
Random Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Network Delay

In this paper, we study the H∞ control problem for Linear Parameter Varying (LPV) discrete systems with random time-varying network delay. The state matrices of LPV discrete systems are deterministic functions and changed with parameters; the range of parameters is measurable. Considering the characteristics of networks with random time-varying delay, we proposed a new parameter-dependent H∞ performance criterion based on the Lyapunov stability theory. The coupling between Lyapunov functions and system matrices could be eliminated by introducing an additional matrix in this criterion, which made it easier for numerical implementation. On this basis, we designed a state feedback controller by virtue of linear matrix inequalities, which transformed the sufficient conditions into existence condition of solution of parametric linear matrix inequalities. The designed controller could keep the closed-loop system asymptotically stable under given time delay and probability and meet predefined performance metric. The validity of the proposed method is verified by numerical simulation.

scholarly journals Lag Synchronization of Hyperchaotic Systems via Intermittent Control

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Junjian Huang ◽  
Chuandong Li ◽  
Wei Zhang ◽  
Pengcheng Wei ◽  
Qi Han
Keyword(s):  
Theoretical Analysis ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Intermittent Control ◽  
Lag Synchronization ◽  
Control Scheme ◽  
Hyperchaotic Systems ◽  
Theoretical Results

Different from the most existing results, in this paper an intermittent control scheme is designed to achieve lag synchronization of coupled hyperchaotic systems. Several sufficient conditions ensuring lag synchronization are proposed by rigorous theoretical analysis with the help of the Lyapunov stability theory. Numerical simulations are also presented to show the effectiveness and feasibility of the theoretical results.

Disturbance-observer-based l2–l∞ control for discrete-time Markovian jump system

2018 ◽  
Vol 40 (9) ◽  
pp. 2807-2812 ◽  
Author(s):  
Linlin Hou ◽  
Haibin Sun
Keyword(s):  
Discrete Time ◽  
Disturbance Observer ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Markovian Jump ◽  
Markovian Jump System ◽  
First Case ◽  
Control Scheme ◽  
Jump Systems

This paper considers the problem of anti-disturbance control for discrete-time Markovian jump systems with multiple disturbances. The controller is constructed via disturbance-observer-based control and l2– l∞ control. The disturbances are divided into two parts. One, in the same channel as the control inputs, is described by an exogenous system. The other is assumed to be bounded with an [Formula: see text] norm. A disturbance observer is presented to estimate and reject the first-case disturbances for discrete-time Markovian jump systems, and an l2– l∞ control scheme is used to attenuate the second-case disturbances. By using linear matrix inequalities, a solvable sufficient condition is developed. Finally, the effectiveness of the proposed control scheme is demonstrated via a numerical example.

Fixed-time tracking control for two-link rigid manipulator based on disturbance observer

2021 ◽  
pp. 014233122098363
Author(s):  
Heli Gao ◽  
Mou Chen
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Tracking Control ◽  
Disturbance Observer ◽  
Inverse Dynamics ◽  
External Disturbance ◽  
Lyapunov Stability Theory ◽  
Fixed Time ◽  
Extended State

This paper studies the fixed-time disturbance estimate and tracking control for two-link manipulators subjected to external disturbance. A fixed-time extended-state disturbance observer (FxTESDO) is proposed by improving the extended state observer. Also, a fixed-time inverse dynamics tracking control (FxTIDTC) scheme based on the FxTESDO is given for two-link manipulators. The fixed-time convergence of the FxTESDO and FxTIDTC is proved by the Lyapunov stability theory and with the aid of the bi-limit homogeneous technique. Numerical simulations are employed to illustrate the effectiveness of the proposed FxTIDTC.

Vibration control of network-based offshore structures subject to earthquakes

2021 ◽  
pp. 014233122110259
Author(s):  
Hua-Nv Feng ◽  
Bao-Lin Zhang ◽  
Yan-Dong Zhao ◽  
Hui Ma ◽  
Hao Su ◽  
...  
Keyword(s):  
Sufficient Conditions ◽  
Offshore Structures ◽  
Delay Systems ◽  
Linear Matrix ◽  
Seismic Responses ◽  
Marine Structures ◽  
Damping Control ◽  
Marine Structure ◽  
Uncertain Model ◽  
Control Scheme

Marine structures are inevitably influenced by parametric perturbations as well as multiple external loadings. Among these loadings, earthquake is generally more destructive and unpredictable than others. It is significant to develop effective active control schemes to guarantee the safety, stability, and integrity of marine structures subject to earthquakes and parametric perturbations. In this paper, the problem of networked [Formula: see text] robust damping control is addressed to stabilize a marine structure subject to earthquakes. First, in consideration of perturbations of the structure parameters, an uncertain model of the networked marine structure under earthquakes is presented. Second, a robust networked [Formula: see text] control scheme is presented to suppress seismic responses of the structure. By using stability theory of time-delay systems, several sufficient conditions on robust stability of the networked marine structure system are obtained, and the linear matrix inequality methods are utilized to solve the gain matrix of the controller. Finally, simulation indicates that compared with the traditional robust [Formula: see text] control and the proposed networked [Formula: see text] control, the seismic responses amplitudes of the marine structure under the two controllers are almost the same, while the latter is more economic than the former.

Adaptive state estimation of Markov switched neural networks driven by Lévy noise

2019 ◽  
Vol 42 (2) ◽  
pp. 330-336
Author(s):  
Dongbing Tong ◽  
Qiaoyu Chen ◽  
Wuneng Zhou ◽  
Yuhua Xu
Keyword(s):  
Neural Networks ◽  
State Estimation ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Lévy Noise ◽  
Linear Matrix ◽  
Delayed Neural Networks ◽  
Switched Neural Networks ◽  
Inequality Technique ◽  
Levy Noise

This paper proposes the [Formula: see text]-matrix method to achieve state estimation in Markov switched neural networks with Lévy noise, and the method is very distinct from the linear matrix inequality technique. Meanwhile, in light of the Lyapunov stability theory, some sufficient conditions of the exponential stability are derived for delayed neural networks, and the adaptive update law is obtained. An example verifies the condition of state estimation and confirms the effectiveness of results.

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