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Exponential stability of Markovian jumping Cohen-Grossberg neural networks with mixed mode-dependent time-delays

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Stability Theory Of Switched Dynamical Systems

Input/output-to-state stability of impulsive switched systems

This paper investigates the stability analysis for a class of discrete-time switched nonlinear time-delay systems. These systems are modelled by a set of delay difference equations, which are represented in the state form. Then, another transformation is made towards an arrow form. Therefore, by applying the Kotelyanski conditions combined to the M−matrix properties, new delay-independent sufficient stability conditions under arbitrary switching which correspond to a Lyapunov function vector are established. The obtained results are explicit and easy to use. A numerical example is provided to show the effectiveness of the developed results.

https://www.tandfonline.com/doi/pdf/10.1080/21642583.2013.879543

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

This paper is concerned with the problems of stability analysis and stabilization with a state feedback controller through pole placement for a class of both continuous and discrete-time switched nonlinear systems These systems are modeled by differential or difference equations Then, a transformation under the arrow form is employed Note that, the main contribution in this work is twofold: firstly, based on the construction of an appropriated common Lyapunov function, as well the use of the vector norms notion, the recourse to the Kotelyanski lemma, the M-matrix proprieties, the aggregation techniques and the application of the Borne-Gentina criterion, new sufficient stability conditions under arbitrary switching for the autonomous system are deduced Secondly, this result is extended for designing a state feedback controller by using pole assignment control, which guarantee that the corresponding closed-loop system is globally asymptotically stable under arbitrary switching The main novelties features of these obtained results are the explicitness and the simplicity in their application Moreover, they allow us to avoid the search of a common Lyapunov function which is a difficult matter Finally, as validation to stabilize a shunt DC motor under variable mechanical loads is performed to demonstrate the effectiveness of the proposed results

Stability and stabilization studies for a class of switched nonlinear systems via vector norms approach.

This paper addresses the stability analysis problem for a class of discrete-time switched nonlinear time-delay systems with polytopic uncertainties. These considered systems are characterized by delayed difference nonlinear equations which are given in the state form representation. Then, a transformation under the arrow form is employed. Indeed, by constructing an appropriated common Lyapunov function, and also by resorting to the Kotelyanski lemma and the M-matrix proprieties, new delay-independent stability conditions under arbitrary switching law are deduced. Compared with the existing results of switched systems, those obtained results are formulated in terms of the unknown polytopic uncertain parameters, explicit and easy to apply. Moreover, this method allows us to avoid the search for a common Lyapunov function which is a difficult matter. Finally, a numerical example is presented to illustrate the effectiveness of the proposed approach.

/pdf/on-stability-analysis-of-discrete-time-uncertain-switched-qq69yxdk0o.pdf

On stability analysis of discrete-time uncertain switched nonlinear time-delay systems

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.

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

This paper addresses the stability problem for a class of switched nonlinear time varying delay systems modeled by delay differential equations. By transforming the system representation under the arrow form and using a new constructed Lyapunov function, the aggregation techniques, the Borne-Gentina practical stability criterion associated with the properties, new delay-independent stability conditions of the considered systems are established. Compared with the existing results in this area, the obtained result is explicit, simple to use and allows us to avoid the problem of searching a common Lyapunov function. Finally, an example is provided, with numerical simulations, to demonstrate the effectiveness of the proposed method.

Marwen Kermani

Papers

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

Stability and stabilization studies for a class of switched nonlinear systems via vector norms approach.

On stability analysis of discrete-time uncertain switched nonlinear time-delay systems

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

On the stability analysis of switched nonlinear systems with time varying delay under arbitrary switching