scholarly journals Stabilization Strategies of Supply Networks with Stochastic Switched Topology

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Shukai Li ◽  
Jianxiong Zhang ◽  
Wansheng Tang
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Control Strategies ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
State Feedback Control ◽  
Disturbance Attenuation ◽  
Supply Networks ◽  
Attenuation Level ◽  
Disturbance Attenuation Level

In this paper, a dynamical supply networks model with stochastic switched topology is presented, in which the stochastic switched topology is dependent on a continuous time Markov process. The goal is to design the state-feedback control strategies to stabilize the dynamical supply networks. Based on Lyapunov stability theory, sufficient conditions for the existence of state feedback control strategies are given in terms of matrix inequalities, which ensure the robust stability of the supply networks at the stationary states and a prescribedH∞disturbance attenuation level with respect to the uncertain demand. A numerical example is given to illustrate the effectiveness of the proposed method.

Fixed-time cluster synchronization in directed community networks with diverse coupling and different-order nodes

2019 ◽  
Vol 33 (08) ◽  
pp. 1950059
Author(s):  
Feilong Zhou ◽  
Yi Zhao ◽  
Shuiming Cai
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Control Strategies ◽  
Sufficient Conditions ◽  
Fixed Time ◽  
State Feedback Control ◽  
Cluster Synchronization ◽  
Community Networks ◽  
Control Schemes ◽  
Different Order

In this paper, fixed-time cluster synchronization of directed community networks (DCNs) with diverse coupling and different-order nodes is explored. For the DCN model, the inherent dynamics and state dimensions of the nodes in different communities can be nonidentical, and moreover, the interactive nodes can differ in their types of connections in different communities and the connections between any pair of different communities can be nonidentical as well. Two types of control strategies, state feedback control and adaptive feedback control, are adopted to force such DCNs to realize cluster synchronization in fixed-time. By utilizing reduction to absurdity, some sufficient conditions ensuring the fixed-time cluster synchronization are derived for the proposed two control schemes. Moreover, it is revealed theoretically that our estimated settling time is more precise and less conservative than that presented in the previous researches. Finally, the validity of the obtained fixed-time cluster synchronization criteria is verified via numerical simulations.

scholarly journals NonlinearL2-Gain Analysis of Hybrid Systems in the Presence of Sliding Modes and Impacts

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
T. Osuna ◽  
O. E. Montano ◽  
Y. Orlov
Keyword(s):  
Sliding Mode ◽  
Numerical Study ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Sliding Modes ◽  
Time Dynamics ◽  
Attenuation Level ◽  
Disturbance Factor ◽  
Disturbance Attenuation Level ◽  
The Impact

TheL2-gain analysis is extended towards hybrid mechanical systems, operating under unilateral constraints and admitting both sliding modes and collision phenomena. Sufficient conditions for such a system to be internally asymptotically stable and to possessL2-gain less than ana priorigiven disturbance attenuation level are derived in terms of two independent inequalities which are imposed on continuous-time dynamics and on discrete disturbance factor that occurs at the collision time instants. The former inequality may be viewed as the Hamilton-Jacobi inequality for discontinuous vector fields, and it is separately specified beyond and along sliding modes, which occur in the system between collisions. Thus interpreted, the former inequality should impose the desired integral input-to-state stability (iISS) property on the Filippov dynamics between collisions whereas the latter inequality is invoked to ensure that the impact dynamics (when the state trajectory hits the unilateral constraint) are input-to-state stable (ISS). These inequalities, being coupled together, form the constructive procedure, effectiveness of which is supported by the numerical study made for an impacting double integrator, driven by a sliding mode controller. Desired disturbance attenuation level is shown to satisfactorily be achieved under external disturbances during the collision-free phase and in the presence of uncertainties in the transition phase.

scholarly journals Fuzzy Logic Maximum Structure and State Feedback Control Strategies of the Electrical Car

2014 ◽  
Vol 50 ◽  
pp. 178-185 ◽  
Author(s):  
O. Kraa ◽  
A. Aboubou ◽  
M. Becherif ◽  
M.Y. Ayad ◽  
R. Saadi ◽  
...  
Keyword(s):  
Fuzzy Logic ◽  
Feedback Control ◽  
State Feedback ◽  
Control Strategies ◽  
State Feedback Control

scholarly journals Mathematical and Dynamic Analysis of a Prey-Predator Model in the Presence of Alternative Prey with Impulsive State Feedback Control

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Chuanjun Dai ◽  
Min Zhao
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Alternative Prey ◽  
Bifurcation Diagrams ◽  
Impulsive State Feedback Control ◽  
Existence And Stability ◽  
Predator Model ◽  
Predator System

The dynamic complexities of a prey-predator system in the presence of alternative prey with impulsive state feedback control are studied analytically and numerically. By using the analogue of the Poincaré criterion, sufficient conditions for the existence and stability of semitrivial periodic solutions can be obtained. Furthermore, the corresponding bifurcation diagrams and phase diagrams are investigated by means of numerical simulations which illustrate the feasibility of the main results.

Robust Observer Based Control for Stability of Linear Systems: Application to Polytopic Systems

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Mouna Belguith ◽  
Amel Benabdallah
Keyword(s):  
Feedback Control ◽  
Output Feedback ◽  
State Feedback ◽  
Linear Time ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Robust Observer ◽  
Linear Time Invariant ◽  
Polytopic Systems ◽  
Linear Time Invariant Systems

This paper investigates the problem of global stabilization by output feedback for linear time-invariant systems. We give first a procedure to design a robust observer for the linear system. Then using this robust observer with the robust state feedback control law developed by Molander and Willems (1980, “Synthesis of State Feedback Control Laws With a Specified Gain and Phase Margin,” IEEE Trans. Autom. Control, 25(5), pp. 928–931), we construct an output feedback which yields a closed loop system with robustness characteristics. That is, we establish a separation principle. Finally, we give sufficient conditions to establish a robust output feedback for linear polytopic systems.

scholarly journals Robust set stabilization of Boolean control networks with impulsive effects

2018 ◽  
Vol 23 (4) ◽  
pp. 553-567 ◽  
Author(s):  
Xiaojing Xu ◽  
Yansheng Liu ◽  
Haitao Li ◽  
Fuad E. Alsaadi
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
State Feedback Control ◽  
Impulsive Effects ◽  
Algebraic Form ◽  
Control Networks ◽  
Set Stabilization ◽  
Necessary And Sufficient

This paper addresses the robust set stabilization problem of Boolean control networks (BCNs) with impulsive effects via the semi-tensor product method. Firstly, the closed-loop system consisting of a BCN with impulsive effects and a given state feedback control is converted into an algebraic form. Secondly, based on the algebraic form, some necessary and sufficient conditions are presented for the robust set stabilization of BCNs with impulsive effects under a given state feedback control and a free-form control sequence, respectively. Thirdly, as applications, some necessary and sufficient conditions are presented for robust partial stabilization and robust output tracking of BCNs with impulsive effects, respectively. The study of two illustrative examples shows that the obtained new results are effective.

scholarly journals Global Mittag–Leffler Stabilization of Fractional-Order BAM Neural Networks with Linear State Feedback Controllers

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Hongyun Yan ◽  
Yuanhua Qiao ◽  
Lijuan Duan ◽  
Ling Zhang
Keyword(s):  
Neural Networks ◽  
Lyapunov Function ◽  
Fractional Order ◽  
State Feedback ◽  
Control Strategies ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Bam Neural Networks ◽  
Linear State ◽  
The Stability

In this paper, the global Mittag–Leffler stabilization of fractional-order BAM neural networks is investigated. First, a new lemma is proposed by using basic inequality to broaden the selection of Lyapunov function. Second, linear state feedback control strategies are designed to induce the stability of fractional-order BAM neural networks. Third, based on constructed Lyapunov function, generalized Gronwall-like inequality, and control strategies, several sufficient conditions for the global Mittag–Leffler stabilization of fractional-order BAM neural networks are established. Finally, a numerical simulation is given to demonstrate the effectiveness of our theoretical results.

State Feedback Control for Fractional Differential Systems with Riemann-Liouville Derivative

2012 ◽  
Vol 562-564 ◽  
pp. 2053-2056
Author(s):  
Yuan Fang
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Feedback Controllers ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Liouville Derivative ◽  
Fractional Differential

This paper studies state feedback control for fractional differential systems with Riemann-Lιiouville derivative, which matrix A not satisfying the condition ιarg(λ(A))ι>α/2 . Based on the state feedback controllers’ designer, and Linear Matrix Inequality (LMI) apαproach, sufficient conditions for the systems with fraction order α (0<α<1) and α (1≤α<2) obtained respectively.

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