Search

During the past decades, much attention has been paid to the stability problem of linear time‐delay systems. In order to obtain tractable stability conditions shown in the linear matrix inequality form, a great number of remarkable results have been reported in the literature. This article first gives a survey of inequality techniques recently developed to estimate integral quadratic terms and reciprocally convex combination terms arising in the estimation of the time derivative of a Lyapunov–Krasovskii functional candidate. Emphases are specially placed on the evolution of various integral and matrix inequalities and the relationships among them. Second, several stability conditions are obtained and carefully compared to illustrate the effectiveness of different inequality techniques on reducing the conservatism. Finally, the quadratic negative‐definiteness lemmas are insightfully reviewed and meanwhile, a simple method to calculate matrix coefficients of a quadratic matrix‐valued function is presented. [ABSTRACT FROM AUTHOR]

Abstract This paper deals with the fuzzy filtering problem for a class of nonlinear time-delay systems described by T-S fuzzy models. Different from the existing schemes in the literature, this paper aims to solve the fuzzy filtering problem by considering the H ∞ , L 2 − L ∞ and dissipative performance constraints in a unified way. To achieve this purpose, the recently proposed notion of extended dissipativity is applied, which provides an inequality covering the well-known H ∞ , L 2 − L ∞ and dissipative performances. Another purpose of this paper is to design filters involving communication delays. Such filters have a more general form than the delay-free filters that have been largely considered in the traditional studies. In order to design the fuzzy filters under consideration, a novel fuzzy Lyapunov-Krasovskii functional is employed, and delay-dependent conditions for stability and performance analysis of the filtering error system are obtained. Then, LMI-based conditions for the existence of the desired filters are presented. The filter parameters can be obtained by solving the presented LMIs. Finally, the effectiveness of the proposed method is substantiated with an illustrative example. Highlights • The extended dissipative fuzzy filtering problems for nonlinear time-delay systems is solved. • The designed filter includes both delayed states and inputs. • Delay-dependent conditions are derived based on a novel Lyapunov-Krasovskii functional. [ABSTRACT FROM AUTHOR]

This paper makes the first attempt to address the global output-feedback tracking control problem for nonlinear systems in the presence of time delay, nonsymmetric input saturation, and external disturbances. As one of the distinctive features, the growth assumptions imposed on system time-delay nonlinearities are removed in this output-feedback case. To handle the unmeasurable states and disturbances, the composite state observer and disturbance observer are constructed simultaneously. Based on these two observers, an output-feedback controller is designed by introducing an auxiliary system to eliminate the effect of input saturation and using a Lyapunov–Krasovskii functional to deal with time delay. It is shown that the designed controller can ensure the closed-loop system to be globally uniformly ultimately bounded. Particularly, instead of converging to an arbitrarily small neighborhood of zero as in related results, the tracking error is proven to be bounded by the saturation input error and design parameters that can be explicitly tuned. Finally, a chemical reactor system is presented to demonstrate the effectiveness and usefulness of the proposed scheme. [ABSTRACT FROM PUBLISHER]

This paper focuses on the design of H ∞ filter and event-triggered scheme for a class of continuous non-linear networked control systems (NCSs) based on fuzzy system appeared with time delays. First, we consider the discrete event-triggered (ET) scheme to make efficient utilisation of bandwidth. Under this ET-scheme, sensor releases the data only when our sampled-data plant violates the specific event-triggered condition. Second, the T-S fuzzy system is used to model the non-linear NCSs. Another purpose of this paper is to design filters involving delays. Such filters have a more general form than the delay-free filters that have been mostly considered in the traditional studies. By using the time-delay system, co-design of event-triggered scheme and H ∞ filter for the delayed NCSs is presented in a unified frame work. To choose the latest data packet and discard the dis-ordered packet logic, zero-order hold is inserted between the fuzzy filter and event generator. Then, by using the novel fuzzy Lyapunov-Krasovskii function approach with free-weighting matrix technique, H ∞ filter design of event-triggered delay NCSs is proposed. Finally, to show the effective result of our co-design method, a tunnel-diode example is given. [ABSTRACT FROM AUTHOR]

The problem of global adaptive state regulation is investigated via output feedback for uncertain feedforward nonlinear time-delay systems. Compared with existing results, our control schemes can be applicable to more general nonlinear time-delay systems because of combining the low-gain scaling approach with the backstepping method. In particular, we allow that there exist uncertain output function and uncertain growth rate imposed on nonlinear terms. Also, one considers a class of nonlinear systems with main-axis delay. By the Lyapunov-Krasovskii theorem, delay-independent controllers are proposed by constructing novel low-gain observers driven by system input, to regulate the states of original system while all the closed-loop signals are globally bounded. Furthermore, two examples are given to illustrate the usefulness of our results. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The problem of H∞ deconvolution filter design for a class of singular Markovian jump systems with time-varying delays and parameter uncertainties is considered in this paper. By constructing a more comprehensive stochastic Lyapunov-Krasovskii functional, novel delay-dependent conditions are established to guarantee the filtering error system is not only stochastically admissible, but also satisfies a prescribed H∞-norm level for all admissible uncertainties. The desired filter parameters can be obtained by solving a set of strict linear matrix inequalities. Two examples and an electrical RLC circuit example are employed to verify the effectiveness and usefulness of the proposed methods in the paper. [ABSTRACT FROM AUTHOR]

SUMMARY This paper is concerned with the reachable set estimation problem for discrete-time linear systems with multiple constant delays and bounded peak inputs. The objective is to check whether there exists a bounded set that contains all the system states under zero initial conditions. First, delay-dependent conditions for the solvability of the addressed problem are derived by employing a novel Lyapunov-Krasovskii functional. The obtained conditions are expressed in terms of matrix inequalities, which are linear when only one scalar variable is fixed. On the basis of these conditions, an ellipsoid containing the reachable set of the considered system is obtained. An approach for determining the smallest ellipsoid is also provided. Second, the approach and results developed in the first stage are generalized to the case of systems with polytopic parameter uncertainties, and delay-dependent conditions are given in the form of relaxed matrix inequalities. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed methods. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This article deals with the problem of passivity analysis for delayed reaction–diffusion bidirectional associative memory (BAM) neural networks with weight uncertainties. By using a new integral inequality, we first present a passivity condition for the nominal networks, and then extend the result to the case with linear fractional weight uncertainties. The proposed conditions are expressed in terms of linear matrix inequalities, and thus can be checked easily. Examples are provided to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM PUBLISHER]

Abstract: This paper is concerned with the passive controller design problem for a class of continuous-time Takagi–Sugeno (T–S) fuzzy systems with both state and input delays. The delays are assumed to be time-varying and differentiable. A notion of very-strict passivity is adopted. The purpose is to design a state-feedback fuzzy controller such that the resulting closed-loop system is very-strictly passive (VSP). Delay-dependent conditions for the solvability of the addressed problem are obtained by applying recently developed techniques for time-delay systems and fuzzy systems. These conditions are expressed by means of strict linear matrix inequalities (LMIs) that can be easily solved. A numerical example and simulation results are provided to demonstrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the problem of absolute exponential stability analysis for a class of continuous-time systems with sector-bounded nonlinearities and interval time-varying delays. Absolute exponential stability criteria, which depend not only on the delay range but also on the decay rate, are derived by using a novel Lyapunov functional. These criteria are expressed in the form of linear matrix inequalities (LMIs) and they can easily be checked. By solving these LMIs, estimates of the exponential decay rate and decay coefficient are obtained. A numerical example is provided to demonstrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: This paper deals with the problem of robust stabilization for uncertain Takagi–Sugeno (T–S) fuzzy systems with constant time delays. The purpose is to design a state-feedback fuzzy controller such that the closed-loop system is robustly exponentially stable with a prescribed decay rate. Sufficient conditions for the solvability of this problem are presented in terms of linear matrix inequalities (LMIs). By using feasible solutions of these LMIs, desired fuzzy controllers are designed and their corresponding exponential estimates are given. In addition, the main results of this paper are explicitly dependent on the decay rate. This enables one to design fuzzy controllers by freely selecting decay rates according to different practical conditions. Two numerical examples are provided finally to demonstrate the effectiveness of the proposed design methods. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the problem of stability analysis for a class of discrete-time recurrent neural networks with time-varying delays. Under a weak assumption on the activation functions and using a new Lyapunov functional, a delay-dependent condition guaranteeing the global exponential stability of the concerned neural network is obtained in terms of a linear matrix inequality. It is shown that this stability condition is less conservative than some previous ones in the literature. When norm-bounded parameter uncertainties appear in a delayed discrete-time recurrent neural network, a delay-dependent robust exponential stability criterion is also presented. Numerical examples are provided to demonstrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

This paper considers the problem of robust exponential stability for a class of recurrent neural networks with time-varying delays and parameter uncertainties. The time delays are not necessarily differentiable and the uncertainties are assumed to be time-varying but norm-bounded. Sufficient conditions, which guarantee that the concerned uncertain delayed neural network is robustly, globally, exponentially stable for all admissible parameter uncertainties, are obtained under a weak assumption on the neuron activation functions. These conditions are dependent on the size of the time delay and expressed in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed stability results. [ABSTRACT FROM AUTHOR]

Highlights • A unified event-triggered network-based model is firstly constructed to study the fault detection problem for positive Markovian systems. • A few scalars guaranteeing positivity are introduced into the fault detection filter model. • The positive Markovian system is modeled to describe the pests' population dynamics, and the results could be applied to pest management. Abstract The problem of event-triggered networked fault detection for positive systems with Markovian parameters is investigated in this paper. A dynamic linear event-triggered scheme is proposed to limit the quantity of the transmitted data in the communication channel. With the consideration of network-induced delays, a networked fault detection filter is designed as a positive Markov jump system to detect the fault signal. ℓ 1 -gain performance is taken into account to study the disturbance attenuation. Through linear Lyapunov function method, the criteria for the solvability of the concerned problem are presented. The parameters of proposed event-triggered condition and desired fault detection filter can be further determined through solving obtained linear programming (LP) problems. Two illustrative examples are given to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper deals with the admissibility analysis and stabilization of stochastic singular Markovian jump systems (SSMJSs) with time delays. More general conditions for the existence and uniqueness of the impulse-free solution to delayed SSMJSs are presented. Consequently, by constructing stochastic Lyapunov–Krasovskii functional and applying generalized Itô formula, new sufficient conditions for the stability of SSMJSs and delayed SSMJSs are obtained in terms of strict linear matrix inequalities. State feedback controller is designed to ensure stabilization of the delayed SSMJSs. Three illustrative examples, including an R L C circuit network and an oil catalytic cracking process, are employed to verify the effectiveness and usefulness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the control design problem for a class of nonlinear systems with the state time-varying time delays and nonsymmetric dead zone. The problem addressed is to design adaptive controllers that guarantee the exact tracking of a given reference signal. Two continuous robust adaptive control schemes are proposed. A positive nonlinear control gain function, which is not required to satisfy an inequality but is expressed explicitly, is carefully constructed and is used in the control law and adaptive law. An illustrative example is provided to demonstrate the validity of the proposed design method. [ABSTRACT FROM AUTHOR]

The problem of state robust H ∞ tracking control for uncertain stochastic systems with interval time-varying delay is considered in this paper. The target is to design a memory state feedback controller such that the resulting closed-loop augmented system is robustly stochastically asymptotically stable and the states of original systems can follow the reference signal with given H ∞ performance. Firstly, by constructing delay-partitioning-dependent Lyapunov–Krasovskii functional with reciprocally convex approach, a delay-dependent condition guaranteeing the robust H ∞ tracking performance is proposed in a set of matrix inequalities. Secondly, new stability criteria for stochastic systems with time-varying delay are given with less conservativeness than some recent results. Thirdly, memory state feedback controller is designed via a set of linear matrix inequalities (LMIs) which can be solved by Matlab LMI toolbox. At last, numerical simulations are addressed to show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]