Varying Delay
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2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Kuan-Yi Lin ◽  
Tung-Sheng Chiang ◽  
Chian-Song Chiu ◽  
Wen-Fong Hu ◽  
Peter Liu

Tracking control for the output using an observer-based H ∞ fuzzy synchronization of time-varying delayed discrete- and continuous-time chaotic systems is proposed in this paper. First, from a practical point of view, the chaotic systems here consider the influence of time-varying delays, disturbances, and immeasurable states. Then, to facilitate a uniform control design approach for both discrete- and continuous-time chaotic systems, the dynamic models along with time-varying delays and disturbances are reformulated using the T-S (Takagi–Sugeno) fuzzy representation. For control design considering immeasurable states, a fuzzy observer achieves master-slave synchronization. Third, combining both a fuzzy observer for state estimation and a controller (solved from generalized kinematic constraints) output tracking can be achieved. To make the design more practical, we also consider differences of antecedent variables between the plant, observer, and controller. Finally, using Lyapunov’s stability approach, the results are sufficient conditions represented as LMIs (linear matrix inequalities). The contributions of the method proposed are threefold: (i) systemic and unified problem formulation of master-slave synchronization and tracking control for both discrete and continuous chaotic systems; (ii) practical consideration of time-varying delay, immeasurable state, different antecedent variables (of plant, observer, and controller), and disturbance in the control problem; and (iii) sufficient conditions from Lyapunov’s stability analysis represented as LMIs which are numerically solvable observer and controller gains from LMIs. We carry out numerical simulations on a chaotic three-dimensional discrete-time system and continuous-time Chua’s circuit. Satisfactory numerical results further show the validity of the theoretical derivations.


Energies ◽  
2021 ◽  
Vol 14 (18) ◽  
pp. 5820
Author(s):  
Wenxi Feng ◽  
Yanshan Xie ◽  
Fei Luo ◽  
Xianyong Zhang ◽  
Wenyong Duan

The stability problem for load frequency control (LFC) of power systems with two time-varying communication delays is studied in this paper. The one-area and two-area LFC systems are considered, respectively, which are modeled as corresponding linear systems with additive time-varying delays. An improved stability criterion is proposed via a modified Lyapunov-Krasovskii functional (LKF) approach. Firstly, an augmented LKF consisting of delay-dependent matrices and some single-integral items containing time-varying delay information in two different delay subintervals is constructed, which makes full use of the coupling information between the system states and time-varying delays. Secondly, the novel negative definite inequality equivalent transformation lemma is used to transform the nonlinear inequality to the linear matrix inequality (LMI) equivalently, which can be easily solved by the MATLAB LMI-Toolbox. Finally, some numerical examples are presented to show the improvement of the proposed approach.


2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Faming Guo ◽  
Ricai Luo ◽  
Xiaolan Qin ◽  
Yunfei Yi

In this paper, we study the problem of exponential stability for the Hopfield neural network with time-varying delays. Different from the existing results, we establish new stability criteria by employing the method of variation of constants and Gronwall’s integral inequality. Finally, we give several examples to show the effectiveness and applicability of the obtained criterion.


PLoS ONE ◽  
2021 ◽  
Vol 16 (9) ◽  
pp. e0256987
Author(s):  
Agnese Venskus ◽  
Francesca Ferri ◽  
Daniele Migliorati ◽  
Sara Spadone ◽  
Marcello Costantini ◽  
...  

The temporal binding window refers to the time frame within which temporal grouping of sensory information takes place. Sense of agency is the feeling of being in control of one’s actions, and their associated outcomes. While previous research has shown that temporal cues and multisensory integration play a role in sense of agency, no studies have directly assessed whether individual differences in the temporal binding window and sense of agency are associated. In all three experiments, to assess sense of agency, participants pressed a button triggering, after a varying delay, the appearance of the circle, and reported their sense of agency over the effect. To assess the temporal binding window a simultaneity judgment task (Experiment 1) and a double-flash illusion task (Experiment 2 and 3) was also performed. As expected, the temporal binding window correlated with the sense of agency window. In Experiment 3, these processes were modulated by applying occipital tACS at either 14Hz or 8Hz. We found 14Hz tACS stimulation was associated with narrower temporal biding window and sense of agency window. Our results suggest the temporal binding window and the time window of sense of agency are related. They also point towards a possible underlying neural mechanism (alpha peak frequency) for this association.


Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2203
Author(s):  
Houssem Jerbi ◽  
Mourad Kchaou ◽  
Attia Boudjemline ◽  
Mohamed Amin Regaieg ◽  
Sondes Ben Aoun ◽  
...  

In this paper, the problem of reliable control design with mixed H∞ /passive performance is discussed for a class of Takagi–Sugeno TS fuzzy descriptor systems with time-varying delay, sensor failure, and randomly occurred non-linearity. Based on the Lyapunov theory, firstly, a less conservative admissible criterion is established by combining the delay decomposition and reciprocally convex approaches. Then, the attention is focused on the design of a reliable static output feedback (SOF) controller with mixed H∞ /passive performance requirements. The key merit of the paper is to propose a simple method to design such a controller since the system output is subject to probabilistic missing data and noise. Using the output vector as a state component, an augmented model is introduced, and sufficient conditions are derived to achieve the desired performance of the closed-loop system. In addition, the cone complementarity linearization (CCL) algorithm is provided to calculate the controller gains. At last, three numerical examples, including computer-simulated truck-trailer and ball and beam systems are given to show the efficacy of our proposed approach, compared with existing ones in the literature.


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