Optimal Parallel Controllers and Filters for a Class of Second-Order Linear Dynamic Systems

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.

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Delay-independent stability criteria under arbitrary switching of a class of switched nonlinear time-delay systems

Kermani

Sakly

2015

Adv Differ Equ

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This paper addresses the stability problem of a class of switched nonlinear time-delay systems modeled by delay differential equations. Indeed, by transforming the system representation under the arrow form, using a constructed Lyapunov function, the aggregation techniques, the Borne-Gentina practical stability criterion associated with the M-matrix properties, new delay-independent conditions to test the global asymptotic stability of the considered systems are established. In addition, these stability conditions are extended to be generalized for switched nonlinear systems with multiple delays. Note that the results obtained are explicit, they are simple to use, and they allow 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.

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Optimal Parallel Controllers and Filters for a Class of Second-Order Linear Dynamic Systems

Cited by 3 publications

References 24 publications

Extensions to Multi-stages and Multi-time Scales

Extensions to Multi-stages and Multi-time Scales

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

Delay-independent stability criteria under arbitrary switching of a class of switched nonlinear time-delay systems

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