Stabilization of discrete-time upper triangular nonlinear cascade systems using cross term constructed Lyapunov functional

Khajepour, Ghasem; Eghtesad, Mohammad; Nami, Mohammad Rahim; Vakilzadeh, Mohsen

doi:10.1016/j.apm.2020.08.016

Cited by 2 publications

(3 citation statements)

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“…This solution was clearly exponentially stable (red in Figure 2). The solution of (45)(46)(47) is not exponentially stable (blue in Figure 2). For the simulation, we take v(t) = 1.25 e −0.5t , v r (t) = e −0.5t , ω(t) = sin(t), ω r (t) = 1 2 sin(t/5) + sin(t), λ = −0.6, while the perturbed term at the jump instants is taken equal to L k (z e (t), θ e (t)) = ( x e sin(θ e ) ).…”

Section: Application: Tracking Controller For Robot Manipulatorsmentioning

confidence: 99%

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Exponential Stability of Impulsive Cascaded Systems and its Application in Robot Control

Dlala

2022

IEEE Access

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In this paper, we study the problem of exponential stability of impulsive cascaded systems.In particular, we provide some sufficient conditions that guarantee the exponential stability of the cascaded systems, provided that the two subsystems are also exponentially stable. The proof of the stability of the cascaded systems is based on the second Lyapunov method and the existence of converse theorems for the stability of impulsive systems. Finally, the usefulness of our results is illustrated by its application to the problem of trajectory tracking for a wheeled robot.INDEX TERMS Cascade impulsive systems, second Lyapunov method, impulsive control.

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Section: Application: Tracking Controller For Robot Manipulatorsmentioning

confidence: 99%

“…The stability of discrete-time cascaded systems was also discussed in [41]- [46]. In [41], a partial state feedback controller design scheme was considered for the study of the global stabilization problem for a class of cascaded nonlinear systems with a time-varying delay.…”

Section: Introductionmentioning

confidence: 99%

Exponential Stability of Impulsive Cascaded Systems and its Application in Robot Control

Dlala

2022

IEEE Access

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“…Gordon and Best 15 applied nonlinear control to road vehicle handling dynamics and evaluated the vehicle performance under conditions of uncertain road friction and rapid changes. Khajepour et al 16 investigated the semi-global practical asymptotic stability of a class of nonlinear cascade systems with upper triangular configuration using cross-term constructed Lyapunov functional. Moosapour et al 17 examined the interference of nonlinear factors and actuator time delay on ABS and then designed a new sliding model control algorithm with an alternative sliding surface to improve the convergence speed.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of the anti-lock braking system with time delay

Gao

Wang

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part I:

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A time delay exists between driver input and vehicle braking state response during the working process of the anti-lock braking system (ABS), and the braking performance of vehicles will be further reduced due to the delay of controllers. This paper investigates a systematic method of stability analysis for time delay ABS, and the analysis focuses on the stability and critical delay algorithm of ABS with delay time. Firstly, the dynamic structure and modelling process of ABS are briefly introduced, and PD control algorithm is adopted to improve the control performance. Then, dynamic models of ABS with time delay are derived, and the full delay stability interval and critical time delay algorithm of ABS are deduced by using the generalized Sturm criterion method. Finally, the validity of the critical delay algorithm by the proposed method and the stability and accuracy of ABS with time delay, different road conditions, vehicle speeds and control parameters are illustrated by numerical simulations, and the results show that the critical time delay algorithm of ABS can be verified under different conditions.

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Stabilization of discrete-time upper triangular nonlinear cascade systems using cross term constructed Lyapunov functional

Cited by 2 publications

References 50 publications

Exponential Stability of Impulsive Cascaded Systems and its Application in Robot Control

Exponential Stability of Impulsive Cascaded Systems and its Application in Robot Control

Stability analysis of the anti-lock braking system with time delay

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