scholarly journals Consensus of Continuous-Time Multiagent Systems with General Linear Dynamics and Nonuniform Sampling

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Yanping Gao ◽  
Bo Liu ◽  
Min Zuo ◽  
Tongqiang Jiang ◽  
Junyan Yu
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
General Linear ◽  
Linear Matrix ◽  
Time Intervals ◽  
Time Dynamics ◽  
Controller Gain ◽  
General Linear Dynamics ◽  
Static Output

This paper studies the consensus problem of multiple agents with general linear continuous-time dynamics. It is assumed that the information transmission among agents is intermittent; namely, each agent can only obtain the information of other agents at some discrete times, where the discrete time intervals may not be equal. Some sufficient conditions for consensus in the cases of state feedback and static output feedback are established, and it is shown that if the controller gain and the upper bound of discrete time intervals satisfy certain linear matrix inequality, then consensus can be reached. Simulations are performed to validate the theoretical results.

CHAOS OF DYNAMICAL SYSTEMS ON GENERAL TIME DOMAINS

2009 ◽  
Vol 19 (11) ◽  
pp. 3829-3832
Author(s):  
ABRAHAM BOYARSKY ◽  
PAWEŁ GÓRA
Keyword(s):  
Dynamical Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Chaotic Map ◽  
Discrete Time System ◽  
Combined System ◽  
Time Intervals ◽  
Time Dynamics ◽  
Time Component ◽  
Time Domains

We consider dynamical systems on time domains that alternate between continuous time intervals and discrete time intervals. The dynamics on the continuous portions may represent species growth when there is population overlap and are governed by differential or partial differential equations. The dynamics across the discrete time intervals are governed by a chaotic map and may represent population growth which is seasonal. We study the long term dynamics of this combined system. We study various conditions on the continuous time dynamics and discrete time dynamics that produce chaos and alternatively nonchaos for the combined system. When the discrete system alone is chaotic we provide a condition on the continuous dynamical component such that the combined system behaves chaotically. We also provide a condition that ensures that if the discrete time system has an absolutely continuous invariant measure so will the combined system. An example based on the logistic continuous time and logistic discrete time component is worked out.

scholarly journals Robust Exponential Stabilization of Uncertain Impulsive Bilinear Time-Delay Systems with Saturating Actuators

2010 ◽  
Vol 2010 ◽  
pp. 1-6 ◽  
Author(s):  
Yang Shujie ◽  
Shi Bao ◽  
Zhang Qiang ◽  
Pan Tetie
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Exponential Stabilization ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Time Dynamics ◽  
Saturating Actuators ◽  
Robust Exponential Stabilization

This paper investigates the problem of robust exponential stabilization for uncertain impulsive bilinear time-delay systems with saturating actuators. By using the Lyapunov function and Razumikhin-type techniques, two classes of impulsive systems are considered: the systems with unstable discrete-time dynamics and the ones with stable discrete-time dynamics. Sufficient conditions for robust stabilization are obtained in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the theoretical results.

Static Output Non-Fragile Control of Fuzzy Bilinear System

2012 ◽  
Vol 198-199 ◽  
pp. 1073-1076
Author(s):  
Guo Zhang ◽  
Yan Hua Zhao
Keyword(s):  
Output Feedback ◽  
Sufficient Conditions ◽  
Output Feedback Control ◽  
Bilinear System ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Controller Gain ◽  
Static Output Feedback Control ◽  
Compensation Approach ◽  
Static Output

This paper focuses on the problem of non-fragile static output feedback control for discrete-time fuzzy bilinear systems. Based on the parallel distributed compensation approach, the sufficient conditions are derived in the presence of the additive controller gain perturbations. The stabilization conditions are further formulated into linear matrix inequalities (LMI) so that the desired controller can be easily obtained by using the LMI toolbox.

scholarly journals Resilient asynchronous H∞ control designed for discrete-time Markov jump systems: Static output feedback case

2018 ◽  
Vol 10 (1) ◽  
pp. 168781401774770
Author(s):  
Xiao Lu ◽  
Lei Yang ◽  
Haixia Wang ◽  
Yuxia Li
Keyword(s):  
Discrete Time ◽  
Output Feedback ◽  
Traffic Control ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Matrix Inequalities ◽  
Markov Jump ◽  
Markov Jump Linear Systems ◽  
Static Output

This article is concerned with the problem of resilient asynchronous H∞ static output feedback control for discrete-time Markov jump linear systems. By Finsler’s Lemma, and with the help of two sets of slack variables, the product terms of system matrices and Lyapunov matrices are decoupled. Resilient asynchronous controller is designed to improve the robustness of the controller and overcome the drawback that the controller cannot get the information of the system’s mode. The controller that makes sure the closed-loop system is stochastically stable and with prescribed H∞ performance is designed. The bilinear matrix inequalities are given as the sufficient conditions for the controller design, which can be solved using linear matrix inequalities along with line search. This control strategy can be used in many practical application fields, such as robot control, aircraft, and traffic control.

Finite-Frequency Static Output Feedback H∞ Control of Continuous-Time T–S Fuzzy Systems

2018 ◽  
Vol 28 (02) ◽  
pp. 1950023 ◽  
Author(s):  
Redouane Chaibi ◽  
Ismail Er Rachid ◽  
El Houssaine Tissir ◽  
Abdelaziz Hmamed
Keyword(s):  
Output Feedback ◽  
Continuous Time ◽  
Fuzzy Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Matrix Inequalities ◽  
Finite Frequency ◽  
Takagi Sugeno ◽  
Static Output

This paper is concerned with finite-frequency static output feedback (SOF) [Formula: see text] control for a class of continuous-time Takagi–Sugeno (T–S) fuzzy systems. With the aid of the generalized Kalman–Yakubovich–Popov (GKYP) lemma, sufficient conditions for the existence of the finite-frequency SOF [Formula: see text] control are presented. The bilinear matrix inequalities are converted to a set of linear matrix inequalities, with the aid of some special derivations. Two practical examples are given to demonstrate the effectiveness of the proposed method.

scholarly journals H∞Control of Singular Markovian Jump Systems with Bounded Transition Probabilities

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Hongsheng Lin ◽  
Ying Li ◽  
Guoliang Wang
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Transition Probabilities ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Singular Markovian Jump Systems ◽  
Jump Systems

This paper discussesH∞control problems of continuous-time and discrete-time singular Markovian jump systems (SMJSs) with bounded transition probabilities. Improved sufficient conditions for continuous-time SMJSs to be regular, impulse free, and stochastically stable withγ-disturbance attenuation are established via less conservative inequality to estimate the transition jump rates, so are the discrete-time SMJSs. With the obtained conditions, the design of a state feedback controller which ensures the resulting closed-loop system to be stochastically admissible and withH∞performance is given in terms of linear matrix inequalities (LMIs). Finally, illustrative examples are presented to show the effectiveness and the benefits of the proposed approaches.

scholarly journals Fuzzy Stabilization for Nonlinear Discrete Ship Steering Stochastic Systems Subject to State Variance and Passivity Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Wen-Jer Chang ◽  
Bo-Jyun Huang ◽  
Po-Hsun Chen
Keyword(s):  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Control Technique ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Ship Steering

For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.

scholarly journals LMI Formulation for Static Output Feedback Design of Discrete-Time Switched Systems

2009 ◽  
Vol 2009 ◽  
pp. 1-7 ◽  
Author(s):  
Selma Ben Attia ◽  
Salah Salhi ◽  
Mekki Ksouri
Keyword(s):  
Discrete Time ◽  
Output Feedback ◽  
Small Degree ◽  
Switched System ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Additional Degree ◽  
Feedback Design ◽  
And Performance ◽  
Static Output

This paper concerns static output feedback design of discrete-time linear switched system using switched Lyapunov functions (SLFs). A new characterization of stability for the switched system under arbitrary switching is first given together with -performance evaluation. The various conditions are given through a family of LMIs (Linear Matrix Inequalities) parameterized by a scalar variable which offers an additional degree of freedom, enabling, at the expense of a relatively small degree of complexity in the numerical treatment (one line search), to provide better results compared to previous one. The control is defined as a switched static output feedback which guarantees stability and -performance for the closed-loop system. A numerical example is presented to illustrate the effectiveness of the proposed conditions.

scholarly journals Nonfragile H∞ Filter Design for Nonlinear Continuous-Time System with Interval Time-Varying Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-17
Author(s):  
Zhongda Lu ◽  
Guoliang Zhang ◽  
Yi Sun ◽  
Jie Sun ◽  
Fangming Jin ◽  
...  
Keyword(s):  
Continuous Time ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Decoupling Method ◽  
Interval Time ◽  
Time Varying Delay ◽  
Error System ◽  
Delay Dependent

This paper investigates nonfragile H∞ filter design for a class of continuous-time delayed Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delays. Filter parameters occur multiplicative gain variations according to the filter’s implementation, to handle this variations, a nonfragile H∞ filter is presented and a novel filtering error system is established. The nonfragile H∞ filter guarantees the filtering error system to be asymptotically stable and satisfies given H∞ performance index. By constructing a novel Lyapunov-Krasovskii function and using the linear matrix inequality (LMI), delay-dependent conditions are exploited to derive sufficient conditions for nonfragile designing H∞ filter. Using new matrix decoupling method to reduce the computational complexity, the filter parameters can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, numerical examples are given to show the effectiveness of the proposed method.

Sign in / Sign up

Export Citation Format

Share Document