This article investigates exponential stability of uncertain discrete‐time nonlinear switched systems with parameter uncertainties and randomly occurring delays via Takagi–Sugeno fuzzy approach. The randomness of time‐varying delay is characterized by introducing a Bernoulli stochastic variable that follows certain probability distribution. By adopting the average dwell‐time approach with Lyapunov–Krasovskii functional and using convex reciprocal lemma, delay‐dependent sufficient conditions for exponential stability of the switched fuzzy system are derived in terms of linear matrix inequalities (LMIs), which can be solved readily using any LMI solvers. Finally, illustrative examples are provided to demonstrate the effectiveness of the proposed approach. © 2014 Wiley Periodicals, Inc. Complexity 20: 49–61, 2015

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This paper is pertained with the synchronization problem for an array of coupled discrete-time complex networks with the presence of both time-varying delays and parameter uncertainties. The time-varying delays are considered both in the network couplings and dynamical nodes. By constructing suitable Lyapunov-Krasovskii functional and utilizing convex reciprocal lemma, new synchronization criteria for the complex networks are established in terms of linear matrix inequalities. Delay-partitioning technique is employed to incur less conservative results. All the results presented here not only depend upon lower and upper bounds of the time-delay, but also the number of delay partitions. Numerical simulations are rendered to exemplify the effectiveness and applicability of the proposed results.

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This paper investigates the guaranteed cost state estimation problem for a class of discrete-time systems based on the Wirtinger-based inequality with randomly occurring delays (RODs) and randomly occurring uncertainties (ROUs). The time-varying delays and parameter uncertainties are considered to occur in random way. Certain mutually uncorrelated Bernoulli-distributed white-noise sequences are included to govern the random occurrences. The cost function is chosen appropriately to guarantee an adequate level of performance. New sufficient conditions are established in terms of linear matrix inequalities to ensure the estimation of state vectors for the given discrete-time system by constructing Lyapunov-Krasovskii functionals and using reciprocally convex lemma. The advantage of using the proposed results is illustrated via numerical examples.

This paper investigates the problem of non-fragile observer design for a class of discrete-time genetic regulatory networks (DGRNs) with time-varying delays and randomly occurring uncertainties. A non-fragile observer is designed, for estimating the true concentration of mRNAs and proteins from available measurement outputs. One important feature of the results obtained that are reported here is that the parameter uncertainties are assumed to be random and their probabilities of occurrence are known a priori. On the basis of the Lyapunov-Krasovskii functional approach and using a convex combination technique, a delay-dependent estimation criterion is established for DGRNs in terms of linear matrix inequalities (LMIs) that can be efficiently solved using any available LMI solver. Finally numerical examples are provided to substantiate the theoretical results.

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