Robust stabilization to non-linear delayed systems via delayed state feedback: the averaging method

2005 ◽  
Vol 279 (3-5) ◽  
pp. 937-953 ◽  
Author(s):  
Z.H. Wang ◽  
H.Y. Hu ◽  
H.L. Wang
Keyword(s):  
State Feedback ◽  
Averaging Method ◽  
Robust Stabilization ◽  
Delayed Systems ◽  
Non Linear ◽  
Delayed State Feedback

scholarly journals Robust stabilization using a sampled-data strategy of uncertain neutral state-delayed systems subject to input limitations

2018 ◽  
Vol 28 (1) ◽  
pp. 111-122 ◽  
Author(s):  
Nabil El Fezazi ◽  
Fatima El Haoussi ◽  
El Houssaine Tissir ◽  
Teresa Alvarez ◽  
Fernando Tadeo
Keyword(s):  
State Feedback ◽  
Initial Conditions ◽  
Robust Stabilization ◽  
Large Set ◽  
Sampled Data ◽  
Neutral Systems ◽  
State Delay ◽  
Delayed Systems ◽  
Stabilizing Controllers ◽  
Weighting Matrix

AbstractStabilization of neutral systems with state delay is considered in the presence of uncertainty and input limitations in magnitude. The proposed solution is based on simultaneously characterizing a set of stabilizing controllers and the associated admissible initial conditions through the use of a free weighting matrix approach. From this mathematical characterization, state feedback gains that ensure a large set of admissible initial conditions are calculated by solving an optimization problem with LMI constraints. Some examples are presented to compare the results with previous approaches in the literature.

scholarly journals Response to perturbation during quiet standing resembles delayed state feedback optimized for performance and robustness

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ambrus Zelei ◽  
John Milton ◽  
Gabor Stepan ◽  
Tamas Insperger
Keyword(s):  
State Feedback ◽  
Postural Sway ◽  
Fast Response ◽  
Neural System ◽  
Feedback Mechanism ◽  
Quiet Standing ◽  
Deterministic Models ◽  
Measured Time ◽  
Delayed State Feedback ◽  
Damped Oscillator

AbstractPostural sway is a result of a complex action–reaction feedback mechanism generated by the interplay between the environment, the sensory perception, the neural system and the musculation. Postural oscillations are complex, possibly even chaotic. Therefore fitting deterministic models on measured time signals is ambiguous. Here we analyse the response to large enough perturbations during quiet standing such that the resulting responses can clearly be distinguished from the local postural sway. Measurements show that typical responses very closely resemble those of a critically damped oscillator. The recovery dynamics are modelled by an inverted pendulum subject to delayed state feedback and is described in the space of the control parameters. We hypothesize that the control gains are tuned such that (H1) the response is at the border of oscillatory and nonoscillatory motion similarly to the critically damped oscillator; (H2) the response is the fastest possible; (H3) the response is a result of a combined optimization of fast response and robustness to sensory perturbations. Parameter fitting shows that H1 and H3 are accepted while H2 is rejected. Thus, the responses of human postural balance to “large” perturbations matches a delayed feedback mechanism that is optimized for a combination of performance and robustness.

Fuzzy observer–based disturbance rejection control for nonlinear fractional-order systems with time-varying delay

2021 ◽  
pp. 107754632110069
Author(s):  
Parvin Mahmoudabadi ◽  
Mahsan Tavakoli-Kakhki
Keyword(s):  
Fractional Order ◽  
Disturbance Rejection ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Delayed Systems ◽  
Fuzzy Observer ◽  
Time Varying Delay ◽  
Takagi Sugeno

In this article, a Takagi–Sugeno fuzzy model is applied to deal with the problem of observer-based control design for nonlinear time-delayed systems with fractional-order [Formula: see text]. By applying the Lyapunov–Krasovskii method, a fuzzy observer–based controller is established to stabilize the time-delayed fractional-order Takagi–Sugeno fuzzy model. Also, the problem of disturbance rejection for the addressed systems is studied via the state-feedback method in the form of a parallel distributed compensation approach. Furthermore, sufficient conditions for the existence of state-feedback gains and observer gains are achieved in the terms of linear matrix inequalities. Finally, two numerical examples are simulated for the validation of the presented methods.

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