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Improved results on exponential stability of discrete-time switched delay systems

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The work is supported by the National Natural Science Foundation of China (11171079) and the Australian Research Council (DP160102819)

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  • In this paper, we study the exponential stability problem of discrete-time switched delay systems. Combining a multiple Lyapunov function method with a mode-dependent average dwell time technique, we develop novel sufficient conditions for exponential stability of the switched delay systems expressed by a set of numerically solvable linear matrix inequalities. Finally, numerical examples are presented to illustrate less conservativeness of the obtained results.

    Mathematics Subject Classification: Primary:58F15, 58F17;Secondary:53C35.


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  • Figure 1.  State trajectories of switched system under ADT switching with $\tau _a = 2$

    Figure 2.  State trajectories of switched system under MDADT switching with $\tau _{a1} = 1, \tau _{a2} = 1, \tau _{a3} = 1, \tau _{a4} = 2$

    Table 1.  Computation Results For The Switched Delay System (9) Under Two Different Switching Schemes

    Switching SchemesADT SwitchingMDADT Switching
    Criteria for controller designTheorem 1 in [19]Theorem 1 in this paper
    Switching signals$\tau _a^* = 0.1175$
    $\mu = 1.1$
    $\lambda \le 1.5$
    $\tau _{a1}^* = 0.0312$, $\tau _{a2}^* = 0.0409$,
    $\tau _{a3}^* = 0.0642$, $\tau _{a4}^* = 0.1175$,
    ${\mu _1} = {\mu _2} = {\mu _3} = {\mu _4} = 1.1$,
    ${\lambda _1} \le 4.6$, ${\lambda _2} \le 3.2$,
    ${\lambda _3} \le 2.1$, ${\lambda _4} \le 1.5$
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