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This paper is concerned with stability of linear discrete time-delay systems. Note that a tighter estimation on a finite-sum term appearing in the forward difference of some Lyapunov functional leads to a less conservative delay-dependent stability criterion. By using Abel lemma, a novel finite-sum inequality is established, which can provide a tighter estimation than the ones in the literature for the finite-sum term. Applying this Abel lemma-based finite-sum inequality, a stability criterion for linear discrete time-delay systems is derived. It is shown through numerical examples that the stability criterion can provide a larger admissible maximum upper bound than stability criteria using a Jensen-type inequality approach and a free-weighting matrix approach. [ABSTRACT FROM AUTHOR]

This paper is concerned with event-based H ∞ filtering for sampled-data systems. First, an event-based data packet processor is introduced to release sampled measurement outputs only if an event condition is violated. As a result, communication resources can be saved significantly while preserving the desired H ∞ performance. Second, the resulting filtering error system is modeled as a system with an interval time-varying delay. By employing the Lyapunov–Krasovskii functional approach, a new bounded real lemma (BRL) is established such that the filtering error system is asymptotically stable with the prescribed H ∞ performance. Third, by performing an invertible linear transformation on the filtering error system, a linear matrix inequality (LMI)-based sufficient condition, which is equivalent to the condition in the BRL, is obtained on the feasibility of the event-based H ∞ filtering problem. Consequently, suitable H ∞ filters and the event parameters in the event condition can be co-designed provided that a set of LMIs are satisfied. Finally, a mechanical system with two masses and two springs is given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the network-based filtering for a stochastic system, where data transmission from the stochastic system to a filter is completed via a communication network. Network-induced delays, packet dropouts and packet disorders are unavoidable due to the use of the network. First, a logic zero-order-hold (ZOH) is designed to discard the disordered packets actively. The network-induced delays and packet dropouts are modeled as an interval time-varying delay. By decomposing the delay interval into subintervals uniformly, the filter to be designed is modeled as a Markov jumping filter with modes governed by a Markov chain. In order to work out the transition rate from one mode to another, a logic jumping-like trigger is embedded into the logic ZOH to simulate the switching of the Markov process. Second, based on the Markov jumping filter model together with a new integral inequality in the stochastic setting, a novel bounded real lemma is presented to ensure that the resultant filtering error system is mean exponentially stable with a prescribed performance. Then, a sufficient condition on the existence of desired Markov jumping filters is provided in terms of a set of linear matrix inequalities. Finally, an air vehicle system is employed to show effectiveness of the proposed design method. [Copyright &y& Elsevier]