Robust exponential stability and stabilisation of parametric uncertain switched linear systems under arbitrary switching

Bagherzadeh, Mohamad Ali; Ghaisari, Jafar; Askari, Javad

doi:10.1049/iet-cta.2015.0185

Cited by 29 publications

(39 citation statements)

References 35 publications

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“…On the basis of the above discussion, there arises a natural question whether one can define a robustness measure of stability (for instance a stability radius) for switched linear systems and, moreover, how to characterise and calculate this measure. To the best of our knowledge, such a question has not been addressed so far in the literature, although different aspects of robust analysis for stability of switched systems has been studied already by the authors [1,2,[13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

On robust stability of switched linear systems

Son

Ngoc

2020

IET Control Theory & Applications

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Section: Introductionmentioning

confidence: 99%

On robust stability of switched linear systems

Son

Ngoc

2020

IET Control Theory & Applications

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“…The most important research direction of switched systems is to investigate the stability of switched systems. There are two aspects of this problem: one is how to obtain stable condition of switched systems under the arbitrary switching law [4][5][6]; the other is how to construct a switching law to guarantee the switched systems to be stable [7,8]. Based on the discussion about the stability, some schemes of controller synthesis have been further put forward [9,10].…”

Section: Introductionmentioning

confidence: 99%

Disturbance Attenuation and Rejection for a Class of Switched Nonlinear Systems Subject to Input and Sensor Saturations

Wei

Sun

Jia

et al. 2019

Mathematical Problems in Engineering

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This paper investigates the problem of disturbance attenuation and rejection for a class of switched nonlinear systems subject to input and sensor saturations, in which exosystem generated disturbances and H2-norm bounded disturbances are considered. The full-order and reduced-order observers are designed according to whether the system states are available or not. Based on the estimating values of the system states and exosystem generated disturbances, the design schemes for the composite controllers are put forward based on the full-order and reduced-order observers, respectively. For a switched system, the input and sensor saturations would influence the effective synthesis of observer and controller. By sector nonlinearity technology, the stability of the augmented closed-loop systems under the proposed composite controllers are analyzed, and the conditions of synthesis of the observers and controllers are further presented to ensure the augmented systems to be robustly asymptotically stable with a weighted H∞ performance level. An example is given to guarantee the effectiveness of the proposed control schemes.

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“…In these cases, in order to keep the system working, the system should be stable under arbitrary switching. A typical approach for the stability analysis of switched dynamical systems with arbitrary switching signal is to search for a suitable common Lyapunov function (CLF) V x such that the rate of the decrease of V x along the trajectories of systems is not affected by switching (see, e.g., [37][38][39][40] and the references therein). If the CLF for the systems does not exist or is not known, in this case, we can study the stability of the system by using multiple Lyapunov functions (MLFs) V p x , p ∈ P , (see [37,41,42]).…”

Section: Introductionmentioning

confidence: 99%

Robust Exponential Stability Analysis of Switched Neural Networks with Interval Parameter Uncertainties and Time Delays

Xue

Peng

et al. 2018

Complexity

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In this paper, the stability of switched neural networks (SNNs) with interval parameter uncertainties and time delays is investigated. First, the conditions for the existence and uniqueness of the equilibrium point of the system are discussed. Second, the average dwell time approach and M-matrix property are employed to obtain conditions to ensure the globally exponential stability of the delayed SNNs under constrained switching. Third, by resorting to inequality technique and the idea of vector Lyapunov function, sufficient condition to ensure the robust exponential stability of the delayed SNNs under arbitrary switching is derived. The form of the constructed Lyapunov functions is simple, which has certain commonality in studying delayed SNNs, and the proposed results not only are explicit but also reveal the relationship between the constrained switching and the arbitrary switching of the SNNs. Finally, two numerical examples are presented to illustrate the effectiveness and less conservativeness of the main results compared with the existing literature.

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Robust exponential stability and stabilisation of parametric uncertain switched linear systems under arbitrary switching

Cited by 29 publications

References 35 publications

On robust stability of switched linear systems

On robust stability of switched linear systems

Disturbance Attenuation and Rejection for a Class of Switched Nonlinear Systems Subject to Input and Sensor Saturations

Robust Exponential Stability Analysis of Switched Neural Networks with Interval Parameter Uncertainties and Time Delays

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