Lyapunov redesign for a class of uncertain systems with delays

Gomez, Marco A.; Cruz-Ancona, Christopher D.

doi:10.1016/j.nahs.2021.101096

Cited by 4 publications

(8 citation statements)

References 19 publications

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“…Within the framework of Sliding Mode Control (SMC), preliminary results addressing the above problem have been recently presented, 16,17 where the departing assumption is that the time-delay system is nominally stabilizable and that there exists a Lyapunov-Krasovskii functional of a certain class associated with the stable nominal system, for example,…”

Section: Definitionmentioning

confidence: 99%

“…They can be found numerically; 15,22 the approach in Reference 22 being within the framework of delay Lyapunov matrices. In contrast with the departing assumptions in previous work, 16,17 Assumption 1 already enables constructing a complete type functional associated to system (2), that satisfies the upper and lower bounds in Lemma 1.…”

Section: A New Class Of Sliding Manifoldsmentioning

confidence: 99%

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Closing the gap from nominal to robust asymptotic stabilization of time delay systems

Gomez,

Cruz‐Ancona

2024

Intl J Robust & Nonlinear

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SummaryThe control problem of a general class of perturbed linear invariant time‐delay systems within the Sliding Mode Control framework is addressed. We introduce a novel class of sliding manifolds with a structure not previously reported in the literature, which constructively emerges from complete type functionals of the corresponding nominal time‐delay systems and depends on the whole state of the system. A fundamental conclusion derived from this proposal is that every time‐delay system with matched perturbations, whose associated nominal system is exponentially stabilizable, is robustly asymptotically stabilizable. In fact, the introduced sliding manifold enables to construct discontinuous and continuous sliding mode control‐based algorithms that mitigate different classes of perturbations.

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Section: Definitionmentioning

confidence: 99%

Section: A New Class Of Sliding Manifoldsmentioning

confidence: 99%

Closing the gap from nominal to robust asymptotic stabilization of time delay systems

Gomez,

Cruz‐Ancona

2024

Intl J Robust & Nonlinear

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“…Eventually, in order to demonstrate the effectiveness of the recommended method, a comparative simulation study between the schemes in [7] and this paper is carried out under the same control objective. As previously mentioned in [7], cross backstepping using conventional TBLF is employed to manage a FIGURE 4 The trajectories of the constrained states using the proposed method FIGURE 5 The trajectories of the free states using the proposed method FIGURE 6 The trajectories of the control inputs using the proposed method FIGURE 7 The trajectories of the control inputs using cross backstepping with TBLF. TBLF, tan-type barrier Lyapunov function.…”

Section: Numerical Examplementioning

confidence: 99%

“…Control for non-linear systems has sparked a lot of interest; hence, numerous control approaches for non-linear systems have been explored. Non-linear systems have been given control methods based on the Lyapunov function, such as sliding mode control (SMC), Lyapunov redesign, and the backstepping method [1][2][3][4].…”

Section: Introductionmentioning

confidence: 99%

Cross backstepping sliding mode control using integral barrier Lyapunov function for cross‐strict feedback systems

Paylakhi

Pariz

Sistani

et al. 2022

IET Control Theory & Appl

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Cross-backstepping control for a type of uncertain non-strict-feedback non-linear systems with time-varying partial state constraints is the main subject of this work. Nonstrict-feedback non-linear systems are partitioned into two strict-feedback non-linear subsystems: constrained subsystem and unconstrained subsystem. An integral barrier Lyapunov function (IBLF) is used in each step of the backstepping design for the constrained subsystem to guarantee the boundedness of the fictional or actual state tracking errors. The effect of uncertainty is reduced using a hybrid cross-backstepping sliding mode control (SMC) technique. The algorithm employs a systematic approach to developing control laws for non-linear systems with matched and unmatched uncertainties. The simulation results of the proposed controller are juxtaposed with those of the cross backstepping with the time-varying barrier Lyapunov function (TVBLF). The results demonstrate the overall better performance of the proposed method.

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“…Among them, the approaches established on the Lyapunov functions and the small-gain condition are the most common. The Lyapunov functions, as the most famous tool, not only guarantee stability but also investigate the robustness and adopt controller, if necessary [13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Small‐gain based stabilizing control for hybrid systems: Application to bipedal walking robot

Khademian,

Rahmani

2024

IET Control Theory & Appl

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This study presents a systematic methodology for developing a stabilizing controller for a general hybrid systems model. The approach is based on utilizing the small‐gain theorem as a means of constructing the Lyapunov function and analyzing the input–output stability of the subsystems in the feedback loop. By considering the control system in a closed‐loop configuration with the hybrid system, the small‐gain theorem can be applied. In this scheme, a dynamic control system is proposed that satisfies the closed‐loop stability conditions. This method applies to various hybrid systems' applications due to its generality. To demonstrate the effectiveness and performance of the proposed control approach, two simulation examples, including a linear hybrid system and a bipedal walking robot, are examined.

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Lyapunov redesign for a class of uncertain systems with delays

Cited by 4 publications

References 19 publications

Closing the gap from nominal to robust asymptotic stabilization of time delay systems

Closing the gap from nominal to robust asymptotic stabilization of time delay systems

Cross backstepping sliding mode control using integral barrier Lyapunov function for cross‐strict feedback systems

Small‐gain based stabilizing control for hybrid systems: Application to bipedal walking robot

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