On the existence of a common Lyapunov function for a family of nonlinear positive systems

Aleksandrov, A. Yu.

doi:10.1016/j.sysconle.2020.104832

Cited by 19 publications

(11 citation statements)

References 17 publications

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“…By taking the derivative of Equation ( 6) and substituting (7) into it, the tracking error dynamics are obtained:…”

Section: Nonlinear Disturbance Observermentioning

confidence: 99%

“…Despite the challenges, stability analysis of switched systems has attracted the interest of many scientists in the last decades. [4][5][6][7] One of the interesting applications of switched systems is in automobile engineering 8,9 ; many control problems in automotive systems are discussed in the literature, such as transient performance and safety analysis, 10 and system speed control systems and rollover mitigation systems. 11 In Reference 10, a switching performance indicator that can be used to evaluate the level of safety during and shortly after a driver-initiated take-over from an autonomous driving system, is presented.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, some complicated systems can be described as switched systems with multiple subsystems, which makes study and analysis easier. Despite the challenges, stability analysis of switched systems has attracted the interest of many scientists in the last decades 4–7 …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust adaptive tracking control for a class of switched time‐delay systems with application of vehicle roll dynamic control

Bagherzadeh

2022

Intl J Robust & Nonlinear

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The problems of stability and robust tracking control for a class of switched nonlinear systems with uncertain input and state delays are investigated in this study. In the presence of unknown functions and external disturbances, an adaptive fuzzy technique based on nonlinear disturbance observer is used to counteract the effects of external disturbances and approximate unknown functions. For this purpose, it is first assumed that a common Lyapunov function exists for the switched system, and then a new common Lyapunov-Krasovskii functional is built using the terms of the hypothetical common Lyapunov function. By employing this new function, the delay-dependent input-to-state stability (ISS) under an arbitrary switching signal is provided. The robust tracking control problem for this system is investigated next. Finally, to assure ISS and robust tracking performance, an adaptive control law is developed that ensures conditions of the aforementioned hypothetical common Lyapunov function. In addition, to demonstrate the efficiency of the proposed strategy, the aforesaid method is applied to a vehicle roll dynamic as well as a mass-spring system.

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“…By taking the derivative of Equation ( 6) and substituting (7) into it, the tracking error dynamics are obtained:…”

Section: Nonlinear Disturbance Observermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Robust adaptive tracking control for a class of switched time‐delay systems with application of vehicle roll dynamic control

Bagherzadeh

2022

Intl J Robust & Nonlinear

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“…In the process of switching, various performance indexes of the switching system become particularly important, so the research methods of each performance index have attracted extensive attention recently [1–3]. For example, in previous works [4, 5], the method of common Lyapunov function used to study the stability of switched systems is proposed. The common Lyapunov function is difficult to obtain, so it is seldom applied in practical systems.…”

Section: Introductionmentioning

confidence: 99%

Nonfragile robust exponential stabilization of nonlinear uncertain switched systems with actuator saturation

Wang

Zhang

2022

Asian Journal of Control

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For nonlinear uncertain switched systems, the problem of how to overcome the controller vulnerability is studied when the actuator saturation is considered. The sufficient condition for guaranteeing nonfragile robust exponential stabilization of the system is derived by using the method of minimum dwell time. Then, a switching law and the nonfragile state feedback controllers are designed such that the closed‐loop system can be robustly exponentially stabilized at the origin. Next, when some scalar parameters of the closed‐loop system are given, the design issue of the nonfragile state feedback controllers, which aim at enlarging the estimation of domain of attraction for closed‐loop system, is transformed into a convex optimization issue with linear matrix inequalities (LMI) constraints. Finally, an example is given to verify the effectiveness of the proposed method.

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“…In a nonlinear fractional-order system, the Lyapunov direct method can be used to research the Mittag-Leffler stability without having to solve the fractional differential equations directly [1,2]. This technique broadens the idea of demonstrating that a model is stable if it contains any Lyapunov function possibility [3]. It can be used to measure the size of a basin of attraction or the rate at which critical point techniques are applied.…”

Section: Introductionmentioning

confidence: 99%

On Fractional Lyapunov Functions of Nonlinear Dynamic Systems and Mittag-Leffler Stability Thereof

2022

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On the existence of a common Lyapunov function for a family of nonlinear positive systems

Cited by 19 publications

References 17 publications

Robust adaptive tracking control for a class of switched time‐delay systems with application of vehicle roll dynamic control

Robust adaptive tracking control for a class of switched time‐delay systems with application of vehicle roll dynamic control

Nonfragile robust exponential stabilization of nonlinear uncertain switched systems with actuator saturation

On Fractional Lyapunov Functions of Nonlinear Dynamic Systems and Mittag-Leffler Stability Thereof

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