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- W2079107651 abstract "The paper by Cao and Xue considers the employment of the extended linear matrix inequality (LMI) approach of Oliveira et al. [1,2] to the stability analysis of linear systems with constant unknown parameters and time-varying delays. Both delay-independent and delay-dependent cases are considered. The extended LMI approach, incorporating additional instrumental matrix variables, opens the door to lower conservatism in the analysis of parameter-dependent systems as well as the synthesis of state-feedback controllers without requiring all plant polytope vertices to share the same Lyapunov matrix in the stability condition. The later point, of course, implies that quadratic stability is not required and thus the results obtained do not suffer from the conservatism that this assumption would induce for systems with constant parameters. Furthermore, at the price of introducing additional scalars ð, dÞ and losing convexity of the analysis problem, synthesis results for state/delayed-state feedback are obtained. As in the finite-dimensional case, the extension of the LMIs for time delay systems can be readily done by introducing new vector variables for signals previously defined from the state (e.g. the state derivative), imposing an algebraic constraint on the vector variables to maintain the system dynamics, and applying Finsler’s lemma [2] (although the paper of Cao and Xue does not precisely follow this formulation). In summary, the paper brings together in an interesting and cogent fashion a number of disparate, recent approaches to systems analysis and controller design so as to tackle a particularly difficult problem in delay-differential systems theory. Of particular interest to the reader may be the development of stability conditions for both the delaydependent and delay-independent cases without any requirement on the rate of change of the delay via Lyapunov–Razumikhin functions. It is interesting to note that for the constant delay case, both the Lyapunov–Krasovskii and Lyapunov–Razumikhin LMI results can be reinterpreted in terms of a scaled small gain condition [3]. For the time-varying delay case," @default.
- W2079107651 created "2016-06-24" @default.
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- W2079107651 date "2005-01-01" @default.
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- W2079107651 title "Discussion on: “Parameter-Dependent Lyapunov Function Approach to Stability Analysis and Design for Uncertain Systems with Time-Varying Delay”" @default.
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- W2079107651 doi "https://doi.org/10.1016/s0947-3580(05)70428-3" @default.
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