Stability analysis for a class of switched nonlinear time-delay systems

Kermani, Marwen; Sakly, Anis

doi:10.1080/21642583.2013.879543

Cited by 33 publications

(24 citation statements)

References 32 publications

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“…Within the frame of studying stability analysis, the vector norms concept has already been introduced in our previous works [23,25,28,31] in reference to the continuous case and [24,27,29,30,32] in reference to the discrete one, in a field related to the study of convergence.…”

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confidence: 99%

“…−0.83 − k 2 22 (.) Now, according to(27),(28),(29),(30) and(31), the vertex matrices in arrow form are the following:M 11 = P −1 = −P 11 (α) = − α 2 + 1.6 + k2 11 (.) α + k 1 11 (.)…”

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confidence: 99%

“…In this paper, we aim to investigate a novel robust stability analysis and a new state feedback robust stabilization by using pole assignment control for both continuous and discrete-time switched linear systems with polytopic uncertainties. Indeed, based on the construction of a common Lyapunov function, the recourse to the Kotelyanski [20] lemma, the M-matrix proprieties [21,22], the aggregations techniques and the vector norm concept [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39], new sufficient conditions for robust stability under arbitrary switching are established Moreover, this approach is extended in the design of a new state feedback robust stabilization by using pole assignment control.…”

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confidence: 99%

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Robust stability and stabilization studies for uncertain switched systems based on vector norms approach

Kermani

Sakly

2014

Int. J. Dynam. Control

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In this paper, we investigate the problems of robust stability and stabilization via a state feedback controller for both continuous and discrete-time switched linear systems with polytopic uncertainties. These considered systems are represented in the state form. Then, a transformation under the arrow form is performed. Thus, based on the construction of a common Lyapunov function associated with the application of the Kotelyanski lemma, the M-matrix proprieties and the aggregation techniques, new sufficient conditions for robust stability and stabilization under arbitrary switching laws are established. It should be pointed out that the obtained results are explicit, easy to apply and formulated in terms of the polytopic uncertainty parameters. In addition, this proposed method allows us to avoid the search of a common Lyapunov function which is a difficult matter. For illustration, a DC motor model with separate excitation under variable mechanical loads is used to show the effectiveness and the potential of the proposed techniques.

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Robust stability and stabilization studies for uncertain switched systems based on vector norms approach

Kermani

Sakly

2014

Int. J. Dynam. Control

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“…Recently, more and more researchers focus on the nonlinear switching ordinary differential equation systems (see, e.g., [6][7][8][9][10][11][12] and references therein). The general nonlinear form is given as follows: = ( ( )) , ∈ [ , +1 ) , = 0, 1, .…”

Section: Introductionmentioning

confidence: 99%

Stability of Stochastic Differential Switching Systems with Time-Delay and Impulsive Effects

Fang

Huang

Tan

2018

Mathematical Problems in Engineering

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This paper studies the stability of hybrid impulsive and switching stochastic neural networks. First, a new type of switching signal is constructed. The stochastic differential switching systems are steerable under the work of the switching signals. Then, using switching Lyapunov function approach, Itô formula, and generalized Halanay's inequality, some global asymptotical and global exponential stability criteria are derived. These criteria improve the existing results on hybrid systems without noises. An example is given to demonstrate the effectiveness of the results.

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“…These network-induced phenomena, if not adequately dealt with, could seriously degrade the system performances. Among others, two frequently investigated network-induced phenomena are packet dropouts [9,23,26,28] and communication delays [2,8,10,17,19,25,30,[33][34][35]. In a networked system, the communication delays are typically random and the delay characteristic varies from sensor to sensor.…”

Section: Introductionmentioning

confidence: 99%

H_∞fault estimation with randomly occurring uncertainties, quantization effects and successive packet dropouts: The finite-horizon case

Wang

Ding

et al. 2014

Int. J. Robust. Nonlinear Control

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In this paper, the finite-horizon H ∞ fault estimation problem is investigated for a class of uncertain nonlinear time-varying systems subject to multiple stochastic delays. The randomly occurring uncertainties (ROUs) enter into the system due to the random fluctuations of network conditions. The measured output is quantized by a logarithmic quantizer before being transmitted to the fault estimator. Also, successive packet dropouts (SPDs) happen when the quantized signals are transmitted through an unreliable network medium. Three mutually independent sets of Bernoullidistributed white sequences are introduced to govern the multiple stochastic delays, ROUs and SPDs. By employing the stochastic analysis approach, some sufficient conditions are established for the desired finite-horizon fault estimator to achieve the specified H ∞ performance. The time-varying parameters of the fault estimator are obtained by solving a set of recursive linear matrix inequalities (RLMIs). Finally, an illustrative numerical example is provided to show the effectiveness of the proposed fault estimation approach.

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Stability analysis for a class of switched nonlinear time-delay systems

Cited by 33 publications

References 32 publications

Robust stability and stabilization studies for uncertain switched systems based on vector norms approach

Robust stability and stabilization studies for uncertain switched systems based on vector norms approach

Stability of Stochastic Differential Switching Systems with Time-Delay and Impulsive Effects

H_∞fault estimation with randomly occurring uncertainties, quantization effects and successive packet dropouts: The finite-horizon case

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Stability analysis for a class of switched nonlinear time-delay systems

Cited by 33 publications

References 32 publications

Robust stability and stabilization studies for uncertain switched systems based on vector norms approach

Robust stability and stabilization studies for uncertain switched systems based on vector norms approach

Stability of Stochastic Differential Switching Systems with Time-Delay and Impulsive Effects

H∞fault estimation with randomly occurring uncertainties, quantization effects and successive packet dropouts: The finite-horizon case

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H_∞fault estimation with randomly occurring uncertainties, quantization effects and successive packet dropouts: The finite-horizon case