scholarly journals Wirtinger-Type Inequality and the Stability Analysis of Delayed Lur'e System

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Zixin Liu ◽  
Jian Yu ◽  
Daoyun Xu ◽  
Dingtao Peng
Keyword(s):  
Type Inequality ◽  
Uncertain System ◽  
Nonlinear Perturbation ◽  
Linear Matrix ◽  
Stable Theory ◽  
Lur’E Systems ◽  
Lur’E System ◽  
Inequality Technique ◽  
The Stability ◽  
Linear Matrix Inequality Technique

This paper proposes a new delay-depended stability criterion for a class of delayed Lur'e systems with sector and slope restricted nonlinear perturbation. The proposed method employs an improved Wirtinger-type inequality for constructing a new Lyapunov functional with triple integral items. By using the convex expression of the nonlinear perturbation function, the original nonlinear Lur'e system is transformed into a linear uncertain system. Based on the Lyapunov stable theory, some novel delay-depended stability criteria for the researched system are established in terms of linear matrix inequality technique. Three numerical examples are presented to illustrate the validity of the main results.

Stability and Robust Stabilization of 2-D Continuous Systems in Roesser Model Based on GKYP Lemma

2017 ◽  
Vol 8 (3) ◽  
pp. 990 ◽  
Author(s):  
Ismail Errachid ◽  
Abdelaziz Hmamed
Keyword(s):  
Robust Stabilization ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Continuous Systems ◽  
Roesser Model ◽  
Model Based ◽  
Inequality Technique ◽  
The Stability ◽  
Conditions Of Stability ◽  
Linear Matrix Inequality Technique

This paper is concerned with the stability and Robust stabilization problem for 2-D continuous systems in Roesser model, based on Generalized Kalman$-$Yakubovich$-$Popov lemma in combination with frequency-partitioning approach. Sufficient conditions of stability of the systems are formulated via linear matrix inequality technique. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.

An Improved Delay-Dependent Stability Criterion for a Class of Lur’e Systems of Neutral Type

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
K. Ramakrishnan ◽  
G. Ray
Keyword(s):  
Stability Analysis ◽  
Stability Criterion ◽  
Time Derivative ◽  
Neutral Type ◽  
Linear Matrix ◽  
Lur’E Systems ◽  
The Stability ◽  
Delay Dependent ◽  
Bounded Nonlinearity ◽  
Delay Dependent Stability

In this paper, we consider the problem of delay-dependent stability of a class of Lur’e systems of neutral type with time-varying delays and sector-bounded nonlinearity using Lyapunov–Krasovskii (LK) functional approach. By using a candidate LK functional in the stability analysis, a less conservative absolute stability criterion is derived in terms of linear matrix inequalities (LMIs). In addition to the LK functional, conservatism in the proposed stability analysis is further reduced by imposing tighter bounding on the time-derivative of the functional without neglecting any useful terms using minimal number of slack matrix variables. The proposed analysis, subsequently, yields a stability criterion in convex LMI framework, and is solved nonconservatively at boundary conditions using standard LMI solvers. The effectiveness of the proposed criterion is demonstrated through a standard numerical example and Chua’s circuit.

Robust H∞ Filtering for Stochastic Networked Control System with Nonlinearities and Missing Measurements

2012 ◽  
Vol 503-504 ◽  
pp. 1458-1462
Author(s):  
Jun Cheng ◽  
Hong Zhu ◽  
Yu Ping Zhang ◽  
Yong Zeng
Keyword(s):  
Control System ◽  
Sufficient Conditions ◽  
Networked Control System ◽  
Networked Control ◽  
Linear Matrix ◽  
Missing Measurements ◽  
Exponentially Stable ◽  
Inequality Technique ◽  
Error System ◽  
Linear Matrix Inequality Technique

This paper investigate the problem of Robust H∞ filtering for stochastic networked control system with nonlinearities and missing measurements. In this paper, missing measurements and nonlinearities are considered. The sufficient conditions for the existence of the filter are given, thus, guaranteeing the filter error system exponentially stable in the mean-square sense and the performance satisfies a prescribed level by employing the new Lyapunov-Krasovskii functional and linear matrix inequality technique, some new sufficient conditions are obtained.

Lagrange Stability Analysis for Power Systems with Time-Varying Delays

2013 ◽  
Vol 336-338 ◽  
pp. 575-580
Author(s):  
Xiao Hong Wang ◽  
Huan Qi ◽  
Xun Cheng Huang
Keyword(s):  
Power Systems ◽  
Electric Power ◽  
Electric Power Systems ◽  
Stable Region ◽  
Linear Matrix ◽  
Time Varying ◽  
Lagrange Stability ◽  
Application Range ◽  
Inequality Technique ◽  
Linear Matrix Inequality Technique

In this paper, we study the global Lagrange stability for delayed electric power systems. Based on the linear matrix inequality technique, the distinguishing principle and its approach of global Lagrange exponential stability for delayed electric power systems are introduced, which are easily verifiable and have a wider application range. Meanwhile, the estimation of the globally exponentially attractive set (i.e. stable region) is also given out. Finally, an example is given and analyzed to demonstrate our results.

Tracking control for the helicopter with time-varying disturbance and input stochastic perturbation

2019 ◽  
Vol 234 (4) ◽  
pp. 961-976
Author(s):  
Yankai Li ◽  
Mou Chen ◽  
Tao Li ◽  
Huijiao Wang
Keyword(s):  
Tracking Control ◽  
Closed Loop ◽  
Controller Design ◽  
Stochastic Perturbation ◽  
Linear Matrix ◽  
Time Varying ◽  
Inequality Technique ◽  
Error System ◽  
Feedforward Controller ◽  
The Stability

In this paper, the tracking control problem is investigated for the helicopter under time-varying disturbance, input stochastic perturbation, and unmeasurable flapping motion states. Firstly, a state observer and a disturbance observer are constructed to estimate the unmeasurable states and the time-varying disturbance, and the estimation of the disturbance is used in the feedforward controller design. Secondly, under the input stochastic perturbation, a feedback controller is constructed to guarantee the stochastic stability of the closed-loop error system. Using the stochastic control theory and the linear matrix inequality technique, the stability of the closed-loop error system is analyzed, and the gain of the controller is acquired via a solvable sufficient condition. Finally, an example is presented to illustrate the effectiveness of the proposed method.

scholarly journals Event-TriggeredH∞Filtering for Multiagent Systems with Markovian Switching Topologies

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Jiahao Li ◽  
Tingting Zhang ◽  
Jinfeng Gao ◽  
Ping Wu
Keyword(s):  
Multiagent Systems ◽  
Sufficient Conditions ◽  
Markovian Switching ◽  
Linear Matrix ◽  
Switching Topologies ◽  
Communication Links ◽  
Inequality Technique ◽  
Error System ◽  
Linear Matrix Inequality Technique ◽  
Event Triggered

This paper is concerned with the problem of event-triggeredH∞filtering for multiagent systems with Markovian switching topologies and network-induced delay. An event-triggered mechanism is given to ease the information transmission. Consider that the network topology is directed in this paper, which represents the communication links among agents. Due to the existence of network-induced delay, the time-delay approach is adopted, which can effectively deal with filtering error system. By constructing a Lyapunov-Krasovskii functional and employing linear matrix inequality technique, sufficient conditions are established to ensure the filtering error system to achieve asymptotically stable withH∞performance index. A simulation example is given to illustrate the effectiveness of the proposed method.

scholarly journals Robust Stochastic Stability Analysis for Uncertain Neutral-Type Delayed Neural Networks Driven by Wiener Process

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Weiwei Zhang ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Wiener Process ◽  
Stochastic Stability ◽  
Neutral Type ◽  
Linear Matrix ◽  
Delayed Neural Networks ◽  
System A ◽  
Inequality Technique ◽  
Stochastic Stability Analysis ◽  
The Stability

The robust stochastic stability for a class of uncertain neutral-type delayed neural networks driven by Wiener process is investigated. By utilizing the Lyapunov-Krasovskii functional and inequality technique, some sufficient criteria are presented in terms of linear matrix inequality (LMI) to ensure the stability of the system. A numerical example is given to illustrate the applicability of the result.

scholarly journals Finite-TimeH∞Filtering for Singular Stochastic Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Caixia Liu ◽  
Yingqi Zhang ◽  
Huixia Sun
Keyword(s):  
Finite Time ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Time Interval ◽  
Inequality Technique ◽  
Error System ◽  
Singular Stochastic Systems ◽  
Finite Time Boundedness ◽  
Bounded Disturbance ◽  
Linear Matrix Inequality Technique

This paper addresses the problem of finite-timeH∞filtering for one family of singular stochastic systems with parametric uncertainties and time-varying norm-bounded disturbance. Initially, the definitions of singular stochastic finite-time boundedness and singular stochasticH∞finite-time boundedness are presented. Then, theH∞filtering is designed for the class of singular stochastic systems with or without uncertain parameters to ensure singular stochastic finite-time boundedness of the filtering error system and satisfy a prescribedH∞performance level in some given finite-time interval. Furthermore, sufficient criteria are presented for the solvability of the filtering problems by employing the linear matrix inequality technique. Finally, numerical examples are given to illustrate the validity of the proposed methodology.

scholarly journals Input-to-State Stabilization of a Class of Uncertain Nonlinear Systems via Observer-Based Event-Triggered Impulsive Control

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Xiangru Xing ◽  
Jin-E Zhang
Keyword(s):  
Nonlinear Systems ◽  
Impulsive Control ◽  
Linear Matrix ◽  
Uncertain Nonlinear Systems ◽  
State Variables ◽  
Parameter Uncertainties ◽  
Exogenous Disturbances ◽  
Inequality Technique ◽  
Linear Matrix Inequality Technique ◽  
Event Triggered

This article concerns the problem of input-to-state stabilization for a group of uncertain nonlinear systems equipped with nonabsolutely available states and exogenous disturbances. To appropriately cope with these partially measurable state variables as well as dramatically minimize controller updating burden and communication costs, an event-triggered mechanism is skillfully devised and an observer-based impulsive controller with the combination of sample control is correspondingly presented. By resorting to the iterative method and Lyapunov technology, some sufficient criteria are established to guarantee the input-to-state stability of the newly uncertain controlled system under the employed controller, in which an innovative approximation condition as to the uncertain term is proposed and the linear matrix inequality technique is utilized for restraining sophisticated parameter uncertainties. Furthermore, the Zeno behavior in the proposed event-triggered strategy is excluded. The control gains and event-triggered mechanism parameters are conjointly designed by resolving some inequalities of linear matrix. Eventually, the availability and feasibility of the achieved theoretical works are elucidated by two simulation examples.

Analysis of Performance Resilience for Discrete-Time Systems With Both Multiplicative and Additive Control Gain Perturbations

2016 ◽  
Author(s):  
Fan Feng ◽  
Susan C. Schneider ◽  
Edwin E. Yaz
Keyword(s):  
Discrete Time ◽  
Linear Matrix ◽  
Analysis Process ◽  
Discrete Time Systems ◽  
Control Gain ◽  
Inequality Technique ◽  
Time Systems ◽  
Analysis Of Performance ◽  
Additive Control ◽  
Linear Matrix Inequality Technique

In this work, a procedure is presented for performance analysis of the resilience property of discrete-time systems with perturbed controller and observer gains. The resilience property is defined in terms of both multiplicative and additive perturbations on the gains so that the closed loop eigenvalues do not leave a specified region in the complex plane. In this work, this region is chosen as a disk in the unit circle. Maximum gain perturbation bounds can be obtained based on the designer’s choices of controller eigenvalue region. The linear matrix inequality technique is used throughout the analysis process. Illustrative examples are included to demonstrate the effectiveness of the proposed methodology. The observer counterpart of the results is also provided in an appendix.

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