The problem of a stability criterion for a class of linear discrete networked control systems with network-induced delay is discussed in this paper. To improve the existing Lyapunov-Krasovskii functional, we introduce a new augmented matrices and utilized an improved finite-sum inequality to deal with some sum-terms appearing in the difference of the Lyapunov-Krasovskii functional. A less conservative stability criterion is obtained for the system comparing to the existing stability results. In addition, the effectiveness of this method was verified by MATLAB LMIs toolboxes and two numerical examples show that the derived stability criterion is less conservative than the existing ones.

In this paper, the problem of stability for linear systems with time-varying delays is investigated. By inequality, Then we obtain a less conservativstability criteria. Finally, The superiority and validity of the propconstructinga suitable augmented Lyapunov-Krasovskii functional and its derivative is estimated by using Jensen integral osed criteria are verified by comparing maximum delay bounds under various conditions via a numerical example.

This paper is concerned with the stabilization problems for a networked control system based on Takagi-Sugeno(T-S) fuzzy model. Under the network environment, compared with premise variables in T-S fuzzy systems, the premise variables in fuzzy rules of controller have different time scales. Then, by utilizing the variation ranges of asynchronous membership functions, a sufficient condition is derived to ensure that the closed-loop system is asymptotically stable with a prescribed H ∞ performance index. A nonlinear mass-spring system is studied to show the effectiveness of the proposed approach.

The sampled-data H∞ filtering for a continuous-time Takagi–Sugeno fuzzy system with an interval time-varying state delay is investigated, where the measurement outputs from the plant to the filter are assumed to be sampled at discrete instants with a variable period. Firstly, by means of a newly proposed inequality bounding technique and a new Lyapunov–Krasovskii functional, the fuzzy sampled-data H∞ filtering performance analysis is carried out such that the resultant filter error system is asymptotically stable with a prescribed H∞ attenuation performance index. Secondly, sufficient conditions on the existence of fuzzy sampled-data H∞ filters are derived in the simultaneous presence of the time-varying state delay and the variable sampling period. The proposed bounding inequality lies in its more tightness and alleviates the enlargement of some inverse "coefficients" resulting from the utilization of the well-known Jensen integral inequality. Compared with some existing Lyapunov–Krasovskii functionals, more information about the relationship among the current state and its delayed state is considered. The upper bound of the derivative of the time-varying state delay is not required to be less than one. Different from some existing results in the literature, by applying the proposed results, each different value of such an upper bound (greater than one) leads to a different H∞ disturbance attenuation level. Finally, a numerical example and a modified continuous stirred tank reactor system are given to show the effectiveness of the proposed results.

This paper deals with the problem of distributed H∞ consensus filtering for a continuous-time Itô-type stochastic system with Wiener process disturbances and Markovian coupling intercommunication delays. The problem is solved based on distributed H∞ filters in combination with consensus strategies. The set of filter nodes form a communication network whose topology is modeled by a directed graph that describes estimates exchanged among neighboring nodes. A refined technique is provided to tackle the complicated coupling of the exchanged estimates in the presence of random coupling intercommunication delays. Moreover, a sufficient condition on the existence of desired distributed H∞ consensus-based filters is established such that the resultant filter error system is mean square exponentially stable with a weighting H∞ consensus performance index. The filter design problem is posed in terms of linear matrix inequalities. Finally an illustrative example is given to show the effectiveness of the proposed filter design method.

The sampled-data H ∞ filtering for a Takagi-Sugeno (T-S) model-based fuzzy system with an interval time-varying state delay and a variable sampling period is considered. A new Lyapunov-Krasovskii functional is constructed by utilizing more information about the system's current state and the delayed state. Based on the new Lyapunov-Krasovskii functional and a novel inequality bounding technique, a suitable sampled-data fuzzy H ∞ filter is designed to ensure the asymptotic stability and prescribed H ∞ attenuation level of the filter error system. A numerical example and a modified continuous stirred tank reactor (CSTR) system are given to illustrate the effectiveness of the proposed method.

The output feedback stabilization of polytopic-type uncertain discrete systems with interval-like time-varying state and input delays is studied. Based on a new bounding inequality technique, combining a parameter-dependent Lyapunov functional, a stability criterion is firstly presented in terms of a set of simple convex feasibility tests. Then, the output feedback stabilization conditions are formulated in the form of non-convex matrix inequalities, of which a feasible solution can be obtained by solving an LMI-based minimization problem. The newly proposed inequality lies in the partitioning idea of the varying interval and shows its more tightness over some existing bounding techniques. No free weighting matrix is involved. Two illustrative examples are finally given to verify the advantage and effectiveness of the proposed method.

In this paper, we concern with robust stability of networked control systems (NCSs) by taking the effects of both the time-varying network-induced delay and data packet dropout into consideration. A new delay decomposition approach to time-varying delay is proposed and an appropriate Lyapunov-Krasovskii functional is constructed to derive some less conservative stability criteria. No slack matrix variable is introduced and overly bounding for some term is avoided. Furthermore, two numerical examples are given to show the effectiveness of the proposed results.

The stability criterion of networked control systems with both the network-induced delays and data packet dropouts is investigated. A Lyapunov-Krasovskii functional candidate, which makes use of the information of the lower, upper bounds and the middle point of the time-varying network-induced delay interval simultaneously, is proposed and a tighter bounding for an integral term of the delay is estimated to drive a less conservative stability condition for networked control systems. No redundant matrix variable is introduced. Finally, two numerical examples are given to show the effectiveness of the proposed stability criterion.

This paper deals with the stability issues of linear systems with interval time-varying delay. Firstly, two kinds of time-varying delay are considered. Then, based on a new delay bisection approach and a tighter bounding inequality, some less conservative stability conditions are proposed, which are effective for both slow and fast time-varying delay. No model transformation and no slack matrix variable are introduced. Furthermore, overly bounding for some cross term is avoided. Finally, two numerical examples are given to show the effectiveness of the proposed results.

This paper is concerned with the problem of the stability of fuzzy systems with interval time-varying delay. The Takagi-Sugeno (T-S) fuzzy models is introduced to approximate the fuzzy systems. A less conservative delay-dependent stability criterion of fuzzy systems is given in the form of linear matrix inequalities. Some free-weighting matrices are introduced to get a less conservative stability criterion. Two numerical examples are also given to show the effectiveness of the proposed stability criterion.

This note is concerned with robust H infin control of linear networked control systems with time-varying network-induced delay and data packet dropout. A new Lyapunov-Krasovskii functional, which makes use of the information of both the lower and upper bounds of the time-varying network-induced delay, is proposed to drive a new delay-dependent H infin stabilization criterion. The criterion is formulated in the form of a non-convex matrix inequality, of which a feasible solution can be obtained by solving a minimization problem in terms of linear matrix inequalities. In order to obtain much less conservative results, a tighter bounding for some term is estimated. Moreover, no slack variable is introduced. Finally, two numerical examples are given to show the effectiveness of the proposed design method.

This paper is concerned with the stability problem for a class of uncertain linear discrete-time systems with time-varying delay. The delay is of an interval-like type, which means that both lower and upper bounds for the time-varying delay are available. The uncertainty under consideration is norm-bounded uncertainty. Based on Lyapunov-Krasovskii functional approach, delay-dependent stability criteria are obtained using a sum inequality which is first introduced and plays an important role in deriving stability conditions. The criteria are formulated in the form of linear matrix inequalities (LMIs). A numerical example is given to show the effectiveness of the proposed criteria.

A delay- and parameter-dependent approach to generalized H2 filtering is proposed for linear continuous-time uncertain systems with multiple time-varying state delays. The uncertain parameters are assumed to reside in a polytope, and the aim is to design a parameter-dependent or a parameter-independent filter such that the filtering error systems are assured to be asymptotically stable and a prescribed generalized H2 performance is guaranteed. The proposed filter design method possesses many advantages, such as the reduced conservatism of the obtained delay-dependent criteria due to adopting the newly established integral-inequality; the proposed new linearization technique and the parameter-dependent design method for the parameter-dependent filters. Both the conditions for the existence of the parameter-dependent and parameter-independent filters are presented in terms of linear matrix inequalities, and convex optimization problems are formulated to design the desired filters. A numerical example is given to illustrate the validity of the proposed design.

ABSTRACTThis paper is concerned with the problem of robust H∞ controller design for a class of uncertain networked control systems (NCSs). The network‐induced delay is of an interval‐like time‐varying type integer, which means that both lower and upper bounds for such a kind of delay are available. The parameter uncertainties are assumed to be normbounded and possibly time‐varying. Based on Lyapunov‐Krasovskii functional approach, a robust H∞ controller for uncertain NCSs is designed by using a sum inequality which is first introduced and plays an important role in deriving the controller. A delay‐dependent condition for the existence of a state feedback controller, which ensures internal asymptotic stability and a prescribed H∞ performance level of the closed‐loop system for all admissible uncertainties, is proposed in terms of a nonlinear matrix inequality which can be solved by a linearization algorithm, and no parameters need to be adjusted. A numerical example about a balancing problem of an inverted pendulum on a cart is given to show the effectiveness of the proposed design method.

This paper is concerned with the delay-dependent robust stability problem for uncertain linear systems with interval time-varying delay. The time-varying delay is assumed to belong to an interval and no restriction on the derivative of the time-varying delay is needed, which allows the delay to be a fast time-varying function. The uncertainty under consideration is norm-bounded, and possibly time-varying, uncertainty. Based on the Lyapunov–Krasovskii functional approach, a stability criterion is derived by introducing some relaxation matrices that can be used to reduce the conservatism of the criteria. Numerical examples are given to demonstrate effectiveness of the proposed method.

This paper is concerned with the problem of observer-based fuzzy stabilization for time-delay systems. The time-delay under consideration is assumed to be a constant time-delay, but not known exactly. A new design method is proposed for an observer-based fuzzy controller with adaptation to the time-delay. The designed controller simultaneously contains both the current and past state information of the systems and can be derived by solving a set of linear matrix inequalities (LMIs). The existence of the controller is equivalent to that of a controller for time-delay systems where the constant time-delay is known exactly. A numerical example is given to illustrate the effectiveness of the design method.

This paper deals with the problem of delay-dependent robust H∞ control for linear time-delay systems with norm-bounded, and possibly time-varying, uncertainty. The time-delay is assumed to be a time-varying continuous function belonging to a given interval, which means that the lower and upper bounds for the time-varying delay are available, and no restriction on the derivative of the time-varying delay is needed, which allows the time-delay to be a fast time-varying function. Based on an integral inequality, which is introduced in this paper, and Lyapunov–Krasovskii functional approach, a delay-dependent bounded real lemma (BRL) is first established without using model transformation and bounding techniques on the related cross product terms. Then employing the obtained BRL, a delay-dependent condition for the existence of a state feedback controller, which ensures asymptotic stability and a prescribed H∞ performance level of the closed-loop systems for all admissible uncertainties, is proposed in terms of a linear matrix inequality (LMI). A numerical example is also given to illustrate the effectiveness of the proposed method.

In these comments, some misleading statements in the above paper have been pointed out and relation results are given.

The dynamic output feedback controller which satisfies the separation principle for linear time-delay systems with delayed state is presented. The observer-based output feedback controller for delay parameter is given if the delay constant is not precisely known for linear time-delay system. The observer-based output feedback controller and the adaptive controller, which satisfy the requirement of the design, can be obtained by solving two Riccati matrix inequalities. The existence of the controller is equivalent to that of controller with known delay constant. A numerical example illustrats the application of the method.