Effects of leakage delay on global asymptotic stability of complex‐valued neural networks with interval time‐varying delays via new complex‐valued Jensen's inequality

This paper investigates the global asymptotic stability analysis for a class of complex‐valued neural networks with leakage delay and interval time‐varying delays. Different from previous literature, some sufficient information on a complex‐valued neuron activation function and interval time‐varying delays has been considered into the record. A suitable Lyapunov‐Krasovskii functional with some delay‐dependent terms is constructed. By applying modern integral inequalities, several sufficient conditions are obtained to guarantee the global asymptotic stability of the addressed system model. All the proposed criteria are formulated in the structure of a complex‐valued linear matrix inequalities technique, which can be checked effortlessly by applying the YALMIP toolbox in MATLAB linear matrix inequality. Finally, two numerical examples with simulation results have been provided to demonstrate the efficiency of the proposed method.     

Robust exponential stability for discrete‐time interval BAM neural networks with delays and Markovian jump parameters

This paper investigates the problem of global robust exponential stability for discrete‐time interval BAM neural networks with mode‐dependent time delays and Markovian jump parameters, by utilizing the Lyapunov–Krasovskii functional combined with the linear matrix inequality (LMI) approach. A new Markov process as discrete‐time, discrete‐state Markov process is considered. An exponential stability performance analysis result is first established for error systems without ignoring any terms in the derivative of Lyapunov functional by considering the relationship between the time‐varying delay and its upper bound. The delay factor depends on the mode of operation. Three numerical examples are given to demonstrate the merits of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

Data‐driven loop‐shaping design of PID controllers for stable plants

In this paper, a loop‐shaping design method of PID controllers is proposed for stable plants under the condition that the plant is linear time invariant and a finite‐time plant response is available. The integral gain of the PID controller is maximized subject to a stability margin constraint, and the optimal solution can be found by linear programming. A filter bank is used for extracting useful information from the finite‐time response data. Numerical examples show that this method is applicable to a wide range of plants including non‐minimum phase and/or time‐delay plants. Copyright © 2013 John Wiley & Sons, Ltd.     

Stability and H∞ performance of multiple‐delay systems with successive delay components

This paper presents a new model for linear time‐delay systems with multiple delayed states where each delay contains finite number of successive components with different time‐varying properties, referred to as multiple‐delay system with successive time‐varying delay components (MDSSTDCs). General stability result and H_∞ performance conditions, under which the MDSSTDCs are asymptotically stable with certain H_∞ disturbance attenuation level, are derived by exploiting a general Lyapunov–Krasovskii functional and by making use of novel techniques for time‐delay systems. The result is applied to two special types of time‐delay systems frequently used in engineering applications and corresponding conditions for stability and H_∞ performance are obtained. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust wide‐area damping controller design for inter‐area oscillations with signals' delay

A new wide‐area damping control strategy is investigated for flexible AC transmission systems (FACTS) device using wide‐area measurement system (WAMS) signals. The purpose is to design a dynamic output wide‐area damping controller (WADC) for improving the stability of interconnected power systems. The time‐varying delay of wide‐area signal is incorporated into the design process, which can effectively reduce the delay effect on the damping performance. First, a discrete‐time plant model with time‐varying delay is established for power systems; then by using the proposed improved free‐weighting matrices (IFWMs) approach and a convex optimization algorithm, a new and less conservative delay‐dependent stability criterion, expressed in the terms of linear matrix inequalities (LMIs), is obtained without ignoring any useful terms on the difference of a Lyapunov function. Detailed case studies on a 4‐machine two‐area benchmark test system and 16‐machine five‐area NETS‐NYPS interconnected system show that the designed WADC can not only maintain effective damping performance under the condition of time‐varying delay but also get the maximum wide‐area time delay. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Design of unknown‐input reduced‐order observers for a class of nonlinear fractional‐order time‐delay systems

This paper considers the design of reduced‐order state observers for fractional‐order time‐delay systems with Lipschitz nonlinearities and unknown inputs. By using the Razumikhin stability theorem and a recent result on the Caputo fractional derivative of a quadratic function, a sufficient condition for the asymptotic stability of the observer error dynamic system is presented. The stability condition is obtained in terms of linear matrix inequalities, which can be effectively solved by using existing convex algorithms. Numerical examples and simulation results are given to illustrate the effectiveness of the proposed design approach.     

Delay‐dependent robust stability analysis for interval neural networks with time‐varying delay

This article deals with the problem of robust stability for interval neural networks with time‐varying delay. By constructing an appropriate Lyapunov–Krasovskii functional, using the S‐procedure and taking the relationship among the time‐varying delay, its upper bound and their difference into account, some linear matrix inequality(LMI) ‐based delay‐dependent stability criteria are obtained without ignoring any terms in the derivative of the Lyapunov–Krasovskii functional. Finally, two numerical examples are given to demonstrate the effectiveness and benefits of the proposed method. © 2011 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Adaptive TS‐FNN control for a class of uncertain multi‐time‐delay systems: The exponentially stable sliding mode‐based approach

This paper presents an adaptive Takagi–Sugeno fuzzy neural network (TS‐FNN) control for a class of multiple time‐delay uncertain nonlinear systems. First, we develop a sliding surface guaranteed to achieve exponential stability while considering mismatched uncertainty and unknown delays. This exponential stability result based on a novel Lyapunov–Krasovskii method is an improvement when compared with traditional schemes where only asymptotic stability is achieved. The stability analysis is transformed into a linear matrix inequalities problem independent of time delays. Then, a sliding mode control‐based TS‐FNN control scheme is proposed to achieve asymptotic stability for the controlled system. Since the TS‐FNN combines TS fuzzy rules and a neural network structure, fewer numbers of fuzzy rules and tuning parameters are used compared with the traditional pure TS fuzzy approach. Moreover, all the fuzzy membership functions are tuned on‐line even in the presence of input uncertainty. Finally, simulation results show the control performance of the proposed scheme. Copyright © 2008 John Wiley & Sons, Ltd.     

An adaptive switching scheme for uncertain discrete time‐delay systems

In this paper, an adaptive switching control algorithm is proposed for the stabilization of uncertain discrete‐time systems with time‐varying delay. It is assumed that the time delay is unknown and time varying, nonetheless bounded with a known bound. It is supposed that the system is highly uncertain, and that a set of controllers are designed (off‐line) to stabilize the system in the whole uncertain parameter space; subsequently, a switching scheme is developed to stabilize the uncertain time‐delay system. A thorough stability analysis for the uncertain time‐delay system under the mentioned control scheme is provided. Furthermore, an upper bound on the allowable rate of change of the system parameters and delay is obtained. Simulation results are presented to show the efficacy of the proposed switching scheme. Copyright © 2008 John Wiley & Sons, Ltd.     

Robust observer‐based control design for uncertain singular systems with time‐delay

This paper is concerned with the stability analysis and robust dynamic output feedback controller synthesis for uncertain continuous singular systems with time‐delay. First, on the basis of the Lyapunov functional method and by resorting to the delay‐partition technique, improved delay‐dependent sufficient conditions are presented to ensure the nominal unforced system to be admissible (i.e., to be regular, impulse‐free, and stable). Second, with the help of the obtained admissibility criterion, an observer‐based controller is designed by solving a set of LMIs. Finally, the validity and applicability of the proposed approach is shown by examples. Copyright © 2013 John Wiley & Sons, Ltd.     

Robust adaptive control for uncertain time‐delay systems

The problem of robust stabilization for uncertain dynamic time‐delay systems is considered. Firstly a class of time‐delay systems with uncertainties bounded by high‐order polynomials and unknown coefficients are considered. The corresponding controller is designed by employing adaptive method. It is shown that the controller designed can render the closed‐loop system uniformly ultimately bounded stable based on Lyapunov–Krasovskii method and Lyapunov stability theory. Then the proposed adaptive idea is applied to stabilizing a class of large‐scale time‐delay systems with strong interconnections. A decentralized feedback adaptive controller is designed which guarantees the closed‐loop large‐scale systems uniformly ultimately bounded stable. Finally, numerical examples are given to show the potential of the proposed techniques. Copyright © 2005 John Wiley & Sons, Ltd.     

Immersion and invariance adaptive control for discrete‐time systems in strict‐feedback form with input delay and disturbances

This work presents a new adaptive control algorithm for a class of discrete‐time systems in strict‐feedback form with input delay and disturbances. The immersion and invariance formulation is used to estimate the disturbances and to compensate the effect of the input delay, resulting in a recursive control law. The stability of the closed‐loop system is studied using Lyapunov functions, and guidelines for tuning the controller parameters are presented. An explicit expression of the control law in the case of multiple simultaneous disturbances is provided for the tracking problem of a pneumatic drive. The effectiveness of the control algorithm is demonstrated with numerical simulations considering disturbances and input‐delay representative of the application.     

Simple and accurate approaches to implement the complex trans‐conductance suited for time‐domain simulators for small‐signal and large‐signal table‐based models

This paper focuses on the implementation of table‐based models of high‐frequency transistors for time‐domain simulators at microwave and mm‐wave frequencies. In this frequency range, the channel is not capable of responding to the excitation instantaneously therefore, a delay‐time exists between the channel response and the channel excitation. This delay is represented by a complex trans‐conductance in terms of circuit elements. The high‐frequency models of transistors are required to have the implementation of complex trans‐conductance, where the complex part accounts mathematically for the delay‐time between the channel response and the channel excitation. This paper presents simple and accurate approaches to incorporate the complex trans‐conductance in both small‐signal and large‐signal table‐based models for time‐domain simulators (MOS‐AK International Meeting. Eindhoven, Netherlands, April 2008). Implementation approach for each model, small‐signal and large‐signal, is presented in separated sections. In the first step, the delay is realized by the introduction of an ideal transmission line between the channel excitation and the channel response. As transmission lines are not generally suitable for time‐domain simulations, a lumped element equivalent network is introduced in the second step. The latter approach is fully compatible with time‐domain simulators but frequency limitation, determined by the delay‐time value itself, is introduced. Then the implementation of the complex trans‐conductance in large‐signal model is introduced. In terms of large‐signal behavior, delay‐time is important to achieve a non‐quasi static model. Yet again there is limitation in terms of the frequency range that is determined by the delay value itself. The methodology is illustrated on the small‐signal and the large‐signal equivalent circuit of a Multi‐Fin MOSFET transistor. Simulations are carried out by Cadence Spectre and Agilent ADS simulators, and comparisons are carried out between the simulation results and the measurements. Copyright © 2010 John Wiley & Sons, Ltd.     

Stability analysis and robust synchronization of fractional‐order competitive neural networks with different time scales and impulsive perturbations

This article mainly examine a class of robust synchronization, global stability criterion, and boundedness analysis for delayed fractional‐order competitive type‐neural networks with impulsive effects and different time scales. Firstly, by endowing the robust analysis skills and a new class of Lyapunov‐Krasovskii functional approach, the error dynamical system is furnished to be a robust adaptive synchronization in the voice of linear matrix inequality (LMI) technique. Secondly, by ignoring the uncertain parameter terms, the existence of equilibrium points are established by means of topological degree properties, and the solution representation of the considered network model are provided. Thirdly, a novel global asymptotic stability condition is proposed in the voice of LMIs, which is less conservative. Finally, our analytical results are justified with two numerical examples with simulations.     

On robust H∞ filtering of uncertain Markovian jump time‐delay systems

This paper is concerned with the problems of stability analysis, H_∞ performance analysis, and robust H_∞ filter design for uncertain Markovian jump linear systems with time‐varying delays. The purpose is to improve the existing results on these problems. Firstly, a new delay‐dependent stability criterion is obtained on the basis of a novel mode‐dependent Lyapunov functional. Secondly, a new delay‐dependent bounded real lemma (BRL) is derived. It is shown that the presented stability criterion and the BRL are less conservative than the existing ones in the literature. Thirdly, with the new BRL, delay‐dependent conditions for the solvability of the addressed H_∞ filtering problem are given. All the results obtained in this paper are expressed by means of strict linear matrix inequalities. Three numerical examples are provided to demonstrate the utility of the proposed methods. Copyright © 2011 John Wiley & Sons, Ltd.     

Pre‐arrangement of solvability,complexity, stability and quality of GPC systems

A design problem of generalized predictive control (GPC) of plants characterized by discrete‐time models with a non‐zero transportation‐delay is considered. Conditions for the existence of the solution of the problem in terms of relevant design parameters (tuning knobs) are proposed and the system characteristics are discussed. Several design hints suitable for such plant models are proposed. Consequently, it is shown that by a suitable choice of the GPC tuning knobs a definite pre‐arrangement of the solvability, complexity, stability and quality (including robustness) of the resultant GPC control systems can be achieved. Some numerical examples are also given to illustrate the design problem and proposed methodology. Copyright © 2002 John Wiley & Sons, Ltd.     

Optimal analog‐to‐digital transformation of fractional‐order Butterworth filter using binomial series expansion with Al‐Alaoui operator

This paper deals with the optimal analog‐to‐digital transformation of fractional‐order Butterworth filter (FOBF) in terms of infinite impulse response templates. The fractional‐order transfer function of the analog FOBF is transformed into its digital counterpart by employing the Binomial series expansion of different truncation orders, based on the Al‐Alaoui operator. This nonoptimal solution is then treated as an initial point for a local search optimizer such as the Nelder–Mead simplex (NMS) algorithm and also injected as a super‐fit individual in the initial population of a global search constrained evolutionary optimization algorithm (CEOA). Design stability and minimum‐phase response constraints are formulated for the super‐fit scheme. Both the techniques demonstrate good modeling performance; however, the super‐fit CEOA can markedly outperform the NMS method as the problem dimensionality increases.     

Adaptive stabilization of uncertain nonlinear time‐delay systems with quantized input and output

This paper investigates the problem of global output feedback stabilization for a class of uncertain nonlinear time‐delay systems with unknown time delay in the states and the input in which both the input and the output are logarithmically quantized. The nonlinear functions of such systems are not completely known and satisfying certain bounded condition depending on the unmeasured states and the input. We construct a new dynamic high‐gain observer where only an output quantization instead of the output is available for measurement to dominate the unknown nonlinear functions view as external disturbances. A scaled change of coordinates and an appropriate Lyapunov‐Krasovskii functional are derived to achieve the global stabilization in the sense that all the states of such systems are defined, bounded in the maximal interval [0, +∞), and converge to the zero equilibrium. A numerical example is provided to illustrate the result.     

Robust input‐output finite‐time filtering for uncertain Markovian jump nonlinear systems with partially known transition probabilities

In this paper, the robust input‐output finite‐time filtering problem is addressed for a class of uncertain Markovian jump nonlinear systems with partially known transition probabilities. Here, the disturbances, uncertainties, state delay, and distributed delays are all taken into account. Both the stochastic finite‐time boundedness and the stochastic input‐output finite‐time stability are introduced to the Markovian jump nonlinear systems with partially known transition probabilities. By constructing a reasonable stochastic Lyapunov functional and using linear matrix inequality techniques, sufficient conditions are established to guarantee the filtering error systems are stochastic finite‐time bounded and stochastic input‐output finite‐time stable, respectively. Finally, 2 examples are provided to illustrate the effectiveness of the proposed methods.     

Adaptive reconfigurable control of systems with time‐varying delay against unknown actuator faults

This work is concerned with the problem of delay‐dependent adaptive fault‐tolerant controller design against unknown actuator faults for linear continuous systems with time‐varying delay. Based on the online estimation of possible faults by discontinuous adaptation law, identification parameters of the adaptive state feedback controller are updated autonomously to compensate the fault effects on the delayed system. For the first time, a convex combination idea and a projection‐type adaptive approach are combined organically to derive the main results. A set of new delay‐dependent reconfigurable stabilization criteria, which guarantee the stability of closed‐loop systems in both fault‐free and faulty cases, is established in terms of linear matrix inequalities. Two numerical instances for linear delayed systems and the linearized model for the lateral motion of Boeing 747 are respectively simulated to illustrate the superiority and the effectiveness of the presented adaptive delay‐dependent results. Copyright © 2013 John Wiley & Sons, Ltd.