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1

On the finite time stabilization via robust control for uncertain disturbed systems

Ordaz Patricio, Alazki Hussain, Sánchez Bonifacio, Ordaz-Oliver Mario

International Journal of Applied Mathematics and Computer Science

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2023

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Vol. 33, no. 1

71--82

EN

This paper deals with the finite-time stabilization problem for a class of uncertain disturbed systems using linear robust control. The proposed algorithm is designed to provide the robustness of a linear feedback control scheme such that system trajectories arrive at a small-size attractive set around an unstable equilibrium in a finite time. To this end, an optimization problem with a linear matrix inequality constraint is presented. This means that the effects of external disturbances, as well as matched and mismatched uncertain dynamics, can be significantly reduced. Finally, the performance of the suggested closed-loop control strategies is shown by the trajectory tracking of an unmanned aerial vehicle flight.

2

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

El Fezazi N., El Haoussi F., Tissir E. H., Alvarez T., Tadeo F.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 1

111--122

EN

Stabilization 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.

3

Robust controlled positive delayed systems with interval parameter uncertainties: A delay uniform decomposition approach

Elloumi W., Mehdi D., Chaabane M.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 3

441--450

EN

This paper is concerned with robust stabilization of continuous linear positive time-delay systems with parametric uncertainties. The delay considered in this work is a bounded time-varying function. Previously, we have demonstrated that the equidistant delay-decomposition technique is less conservative when it is applied to linear positive time-delay systems. Thus, we use simply a delay bi-decomposition in an appropriate Lyapunov–Krasovskii functional. By using classical and partitioned control gains, the state-feedback controllers developed in our work are formulated in terms of linear matrix inequalities. The efficiency of the proposed robust control laws is illustrated with via an example.

4

Robust soft variable structure control of perturbed singular systems with constrained input

Asadinia M. S., Binazadeh T.

Control and Cybernetics

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2017

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Vol. 46, no. 4

345--360

EN

This paper investigates the robust soft variable structure (RSVS) control technique for perturbed singular systems with constrained input control. The aim of the RSVS control law, in addition to achieving desirable control performance for the constrained input, is the robust stability of the closed-loop system in the presence of perturbation. In this paper, the RSVS control for perturbed singular systems is designed for two cases. First, it is assumed that the perturbation term vanishes at the origin. In this case, the proposed RSVS controller leads to asymptotic stabilization of the perturbed singular system. In the second case, the perturbed singular systems with non-vanishing perturbation are considered and the robustness of RSVS is also investigated. In this situation, the proposed controller guarantees practical stability of the perturbed singular system. Finally, computer simulations are provided for two examples to verify the theoretical results.

5

Hybrid robust stabilization in the Martinet case

Prieur C., Trelat E.

Control and Cybernetics

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2006

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Vol. 35, no 4

923-945

EN

In a previous work, Prieur, Trelat (2006), we derived a result of semi-global minimal time robust stabilization for analytic control systems with controls entering linearly, by means of a hybrid state feedback law, under the main assumption of the absence of minimal time singular trajectories. In this paper, we investigate the Martinet case, which is a model case in 1R3, where singular mini-mizers appear, and show that such a stabilization result still holds. Namely, we prove that the solutions of the closed-loop system converge to the origin in quasi minimal time (for a given bound on the controller) with a robustness property with respect to small measurement noise, external disturbances and actuator errors.

6

Adaptive state feedback control for a class of linear systems with unknown bounds of uncertainties.

Fenlin L., Hao W., Qingxian W., Mingwu S., Siying Z.

Systems Science

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2001

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Vol. 27, nr 3

23-34

EN

The problem of adaptive robust stabilization for a class of linear time-varying systems with disturbance and nonlinear uncertainties is considered. The bounds of the disturbance and uncertainties are assumed to be unknown, being even arbitrary. For such uncertain dynamical systems, the adaptive robust state feedback controller is obtained. And the resulting closed-loop systems are asymptotically stable in theory. Moreover, an adaptive robust state feedback control scheme is given. The scheme ensures the closed-loop systems exponentially practically stable and can be used in practical engineering. Finally, simulations show that the control scheme is effective.