scholarly journals Intra-layer Synchronization in a Duplex Networks with Noise

2021 ◽  
Author(s):  
Jinsen Zhuang ◽  
Yan Zhou ◽  
Yonghui Xia
Keyword(s):  
Dynamical System ◽  
State Feedback ◽  
Feedback Controller ◽  
The Other ◽  
Time Varying ◽  
Stochastic Perturbations ◽  
State Feedback Controller ◽  
Control Schemes ◽  
Simulation Results ◽  
The Impact

This paper concerns the impact of stochastic perturbations on the intra-layer synchronization of the duplex networks. A duplex network contains two layers ([1,2]). Different from the previous works, environmental noise is introduced into the dynamical system of the duplex network. We incorporate both the inter-layer delay and the intra-layer delay into the dynamical system. Both of the delays are time-varying. However, the paper [1] only considered the intra-layer delays and they are assumed as the constants. While the paper [2] did not consider the inter-layer delay or intra-layer delay. When the system does not achieve automatic intra-layer synchronization, we introduce two controllers: one is the state-feedback controller, the other is the adaptive state-feedback controller. Interestingly, we find that the intra-layer synchronization will achieve automatically if the inter-layer coupling strength $c_1$ is large enough when the time-varying inter-layer delays are absent. Finally, some interesting simulation results are obtained for the Chua-Chua chaotic system with application of our theoretic results, which show the feasibility effectiveness of our control schemes.

scholarly journals Robust Position Control of a Two-Sided 1-DoF Impacting Mechanical Oscillator Subject to an External Persistent Disturbance by Means of a State-Feedback Controller

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Firas Turki ◽  
Hassène Gritli ◽  
Safya Belghith
Keyword(s):  
State Feedback ◽  
Position Control ◽  
External Disturbance ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Mechanical Oscillator ◽  
Impact Oscillator ◽  
State Feedback Controller ◽  
The Impact

This paper proposes a state-feedback controller using the linear matrix inequality (LMI) approach for the robust position control of a 1-DoF, periodically forced, impact mechanical oscillator subject to asymmetric two-sided rigid end-stops. The periodic forcing input is considered as a persistent external disturbance. The motion of the impacting oscillator is modeled by an impulsive hybrid dynamics. Thus, the control problem of the impact oscillator is recast as a problem of the robust control of such disturbed impulsive hybrid system. To synthesize stability conditions, we introduce the S-procedure and the Finsler lemmas by only considering the region within which the state evolves. We show that the stability conditions are first expressed in terms of bilinear matrix inequalities (BMIs). Using some technical lemmas, we convert these BMIs into LMIs. Finally, some numerical results and simulations are given. We show the effectiveness of the designed state-feedback controller in the robust stabilization of the position of the impact mechanical oscillator under the disturbance.

Adaptive state-feedback stabilization of stochastic nonholonomic systems with an unknown time-varying delay and perturbations

2020 ◽  
pp. 014233122097417
Author(s):  
Qinghui Du
Keyword(s):  
State Feedback ◽  
Nonholonomic Systems ◽  
Feedback Stabilization ◽  
Feedback Controller ◽  
Input State ◽  
Time Varying ◽  
Initial State ◽  
State Feedback Controller ◽  
Time Varying Delay ◽  
Varying Delay

The problem of adaptive state-feedback stabilization of stochastic nonholonomic systems with an unknown time-varying delay and perturbations is studied in this paper. Without imposing any assumptions on the time-varying delay, an adaptive state-feedback controller is skillfully designed by using the input-state scaling technique and an adaptive backstepping control approach. Then, by adopting the switching strategy to eliminate the phenomenon of uncontrollability, the proposed adaptive state-feedback controller can guarantee that the closed-loop system has an almost surely unique solution for any initial state, and the equilibrium of interest is globally asymptotically stable in probability. Finally, the simulation example shows the effectiveness of the proposed scheme.

scholarly journals Memory State Feedback Control for Time-Varying Delay Switched Fuzzy Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Le Zhang ◽  
Meiyu Jia ◽  
Hong Yang ◽  
Gang Wu
Keyword(s):  
Fuzzy Systems ◽  
State Feedback ◽  
Feedback Controller ◽  
State Feedback Control ◽  
Time Varying ◽  
Memory State ◽  
State Feedback Controller ◽  
Time Varying Delay ◽  
Memory State Feedback ◽  
Varying Delay

Consider the problem of memoryless state feedback controller for time-delay system, which cannot consider both the memoryless and the memory items in the system. Therefore, the memoryless state feedback controller has certain limitations and is more conservative. This paper addresses the memory state feedback control for the time-varying delay switched fuzzy systems based on T-S fuzzy model to overcome the problem discussed above. The state vector and input of the time-varying delay systems contain unknown time-varying delay with known bounds. The designed controller whose parameters are solvable can introduce past state information and reduce the system conservativeness. The more general Lyapunov-Krasovskii functional is selected and the switching law is designed in order to analyze the open-loop system stability, and the memory state feedback controller is designed for the closed-loop system and the criterion for its asymptotic stability. Discuss the solvability of the above two criteria. Finally, a numerical example is given. The simulation results show that the proposed method is more feasible and effective.

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