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This paper is concerned with stability of a linear system with a time-varying delay. First, an improved reciprocally convex inequality including some existing ones as its special cases is derived. Compared with an extended reciprocally convex inequality recently reported, the improved reciprocally convex inequality can provide a maximum lower bound with less slack matrix variables for some reciprocally convex combinations. Second, an augmented Lyapunov–Krasovskii functional is tailored for the use of a second-order Bessel–Legendre inequality. Third, a stability criterion is derived by employing the proposed reciprocally convex inequality and the augmented Lyapunov–Krasovskii functional. Finally, two well-studied numerical examples are given to show that the obtained stability criterion can produce a larger upper bound of the time-varying delay than some existing criteria. [ABSTRACT FROM AUTHOR]

Recent research has shown that one can obtain a less conservative stability criterion for a continuous-time linear system with a time-varying delay by introducing a Lyapunov-Krasovskii functional with a polynomial matrix on the time-varying delay. This paper aims at analysing the stability of discrete-time linear systems with time-varying delays by introducing a delay-square-dependent Lyapunov functional. A novel convex method is presented to formulate a less conservative stability criterion, which is demonstrated through numerical simulation. Moreover, it is also shown that, if the polynomial inequality method is employed, the resultant stability criterion is inapplicable due to its extremely high numerical complexity. [ABSTRACT FROM AUTHOR]

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]

This paper is concerned with the H ∞ performance of discrete-time networked systems subject to network-induced delays and malicious packet dropouts. First, the introduction of a data packet processor enables us to calculate both network-induced delays and the number of consecutive malicious packet dropouts explicitly. Second, a novel Lyapunov functional is constructed, whose forward difference along with the trajectory of the closed-loop system is estimated as a quartic polynomial. A class of necessary and sufficient conditions on such an inequality are established by using the Finsler lemma. By employing the Lyapunov method, a bounded real condition is formulated, which depends on the upper bound of network-induced delays and the maximum number of consecutive malicious packet dropouts. Therefore, their effects on H ∞ performance can be investigated simultaneously. Finally, the effectiveness of the proposed method is shown through an inverted pendulum system. [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]

Abstract: This paper deals with the problem of delay-dependent robust filtering for uncertain linear systems with time-varying delay. Two cases of time-varying delays are fully considered; one is the time-varying delay being continuous uniformly bounded while the other is the time-varying delay being differentiable uniformly bounded with delay-derivative bounded by a constant. A stable linear filter is designed to ensure that the filtering error system is asymptotically stable with a prescribed level of noise attenuation. Based on a new integral inequality, delay-dependent sufficient conditions for the existence of such a filter are established in terms of linear matrix inequalities (LMIs). Through deriving these conditions, neither model transformation nor bounding technique for cross terms is employed. Moreover, the relationship between the sufficient conditions for the two cases of time-varying delay is disclosed. Finally, two examples are also given to illustrate the effectiveness of the proposed methodology. [Copyright &y& Elsevier]

Abstract: The integral-inequality method is a new way of tackling the delay-dependent stabilization problem for a linear system with time-varying state and input delays: . In this paper, a new integral inequality for quadratic terms is first established. Then, it is used to obtain a new state- and input-delay-dependent criterion that ensures the stability of the closed-loop system with a memoryless state feedback controller. Finally, some numerical examples are presented to demonstrate that control systems designed based on the criterion are effective, even though neither nor is stabilizable. [Copyright &y& Elsevier]

This paper is concerned with sufficient conditions for a class of matrix-valued polynomial inequalities on closed intervals and their application to H ∞ filtering for linear systems with time-varying delays. First, a class of higher degree matrix-valued polynomial inequalities are transformed into the first degree matrix-valued polynomial inequalities by introducing some slack matrices. As a result, a convex property is applied to derive sufficient conditions for a class of higher degree matrix-valued polynomial inequalities on closed intervals. Second, by choosing a Lyapunov–Krasovskii functional with a quadratic matrix-valued polynomial on a time-varying delay, and estimating its time-derivative as a third-degree matrix-valued polynomial on the time-varying delay, the proposed sufficient conditions are utilized to formulate a novel bounded real lemma on the existence of H ∞ filters for time-delay systems. Third, some algorithms to filter design are provided and discussed in detail. It is pointed out that, if the filter gain is derived through a generalized inverse matrix method, it may be a fake solution, which is demonstrated through a liquid monopropellant rocket motor with a pressure feeding system. [ABSTRACT FROM AUTHOR]

This paper is concerned with distributed attack detection for a discrete time-varying system monitored by a sensor network. An adversary simultaneously launches distinct data deception attacks on both the system dynamics and sensor intercommunication links so as to intentionally falsify the system state and the exchanged sensor measurement outputs. First, delicate distributed estimators are constructed, aiming to provide resilient local estimates for unavailable system state and appropriate residuals for attack detection. Second, an auxiliary Krein space state–space model as well as innovation analysis and a projection technique is skillfully employed to cast the finite horizon distributed estimator design problem into a minimization problem of a certain indefinite quadratic form. A necessary and sufficient condition on the existence of the minimum is derived. Third, a computational efficient recursive algorithm is developed to design desired distributed estimators such that the local estimates and residuals can be both determined at each time step. Furthermore, a two-stage distributed detection mechanism is proposed for each estimator to alert the attack occurrence. Specifically, it is shown that by properly choosing a weighting matrix parameter, each estimator can respectively detect the deception attacks launched on the system layer and sensor intercommunication links. Finally, the effectiveness of the proposed approach is demonstrated through numerical verification. [ABSTRACT FROM AUTHOR]