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Based on a sliding mode control, a multi‐area decentralised load frequency control power system with time‐varying delays and non‐linear perturbations is designed in this study. Due to the destabilising effect of delay on the global system, it is necessary to design a control system to accommodate vast time delays so as to manage the deviation in frequency and interchange power. By taking advantage of the system structure and disturbance bounds, robustness is improved. A sliding surface is designed, and the stability of the corresponding sliding motion is analysed based on Lyapunov–Razumikhin function. A delay dependent decentralised sliding mode control is synthesised to drive the system to the sliding surface and maintain a sliding motion afterwards. The obtained results are applied to a two‐area interconnected power system to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this study, the exponential stability problem of impulsive system is investigated via sampled‐data control in the presence of random time‐varying delays and non‐linear perturbations. In particular, the time delays are considered to be randomly time varying and they obey the Bernoulli distributions. The authors' main attention is focused on the design of a sampled‐data controller to ensure an exponential stability for the closed‐loop system. By extending the first‐ and second‐order reciprocal convex approach, an efficient method called third‐order reciprocal convex technique is used to manipulate the main results. Through the construction of a suitable Lyapunov–Krasovskii functional combined with input delay approach and Briat lemma, several delay‐dependent sufficient conditions for the concerned system are derived in the form of linear matrix inequalities which can be readily solved by utilising the valid software packages. Some numerical examples are given to illustrate the effectiveness of the developed control technique. [ABSTRACT FROM AUTHOR]

This study deals with the problem of robust stabilisation for non‐linear time‐delay semi‐Markovian jump systems via sliding mode control (SMC). Such a switching is governed by a semi‐Markovian process which is time‐varying and dependent on the sojourn‐time h. The time delay is considered as time‐varying and meets the requirements of the upper and lower bounds. By introducing free‐connection weighting matrix method and Lyapunov functional, sufficient conditions for the resulting sliding mode dynamics in the form of linear matrix inequalities are derived to guarantee the closed‐loop system robustly stochastically stable for all admissible uncertainties and non‐linear perturbations. Then, an SMC law is synthesised to drive the system trajectories onto the predefined switching surface in a finite time. Finally, an example illustrates the validity of the obtained results. [ABSTRACT FROM AUTHOR]

This study is concerned with the problem of robust H∞ sliding mode control (SMC) of It o^ stochastic delayed Markovian jump systems subject to parameter uncertainties and non‐linear perturbations. Firstly, for the sake of practicality, a common integral sliding surface functional without time‐varying delay is proposed. Then, by using linear matrix inequalities technique, sufficient condition for the robust mean‐square exponential stability of the resulting closed‐loop system with a prescribed disturbance attenuation level γ is derived. Moreover, a novel sliding mode controller is designed such that system trajectories can be kept on the sliding surface almost surely since the initial time. Finally, an example is provided to illustrate the effectiveness of the obtained result. [ABSTRACT FROM AUTHOR]

This article reports on an investigation into robust guaranteed cost control (GCC) for uncertain switched neutral systems (USNSs) with interval time-varying mixed delays and nonlinear perturbations via dynamic output feedback. Delay-dependent sufficient conditions are suggested to guarantee the robust exponential stability and to obtain robust GCC for USNSs using the average dwell time approach and the piecewise Lyapunov function technique in terms of a set of linear matrix inequalities. The problem of uncertainty in the system model is solved by deploying the Yakubovich lemma. Lastly, two examples (i.e., a numerical example and the water-quality dynamic model for the Nile River) are given to verify the efficiency of the propounded theories. © 2016 Wiley Periodicals, Inc. Complexity 21: 555-578, 2016 [ABSTRACT FROM AUTHOR]

The problem of finite‐time stability for uncertain time‐varying delay systems with non‐linear perturbations and parametric uncertainties and switched time‐delay systems is studied. New integral inequality with exponential function is proposed to solve the stability problem. By using a suitable form of Lyapunov–Krasovskii‐like functional (LKLF) with exponential function, the integral inequality and estimations of LKLF in the initial and the current time, new delay‐dependent and less conservative stability criteria have been derived in terms of linear matrix inequalities. The average dwell time approach is used to study the FTS of switched time‐delay systems. Five numerical examples are given to show the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper investigates almost sure exponential stability and feedback stabilization for switched time-delay systems with nonlinear stochastic perturbations. The main contributions of this paper are threefold: (i) based on the non-convolution type multiple Lyapunov functionals and the mathematical induction approach, a mean-square exponential stability condition for nonlinear stochastic switched systems is first established, such that the obtained average dwell time does not rely on any given decay rate; (ii) by using the method developed in part (i) and the stochastic analysis techniques and limit methods in probability, an almost sure exponential stability criterion for switched delayed systems with nonlinear stochastic uncertainties is presented, and then a state feedback controller for the systems under consideration is designed; and (iii) when certain assumptions are made on the nonlinear stochastic perturbations, the results in this paper are further improved by relaxing some conditions. The effectiveness of the proposed method is demonstrated by three illustrative examples. [ABSTRACT FROM AUTHOR]

This paper addresses the stabilization problem of neutral systems. The neutral systems assumed to be subjected to nonlinear perturbations and mixed time-varying delays. Specifically, the adaptive control method is used to stabilize the unknown neutral systems. If the system states and the delayed states with its derivatives are available for measurement, a new and less conservative adaptive control algorithm is proposed, and sufficient conditions for the existence of the adaptive control are derived based on Lyapunov's stability theory. The main idea is to make all the stability conditions of the system depend on desired arbitrary matrices, not on the given system matrices. This is accomplished by the adaptation process. Illustrative examples with numerical simulations are studied. The simulation results show the effectiveness of the proposed design methods. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of μ-stability of impulsive differential systems with unbounded time-varying delays and nonlinear perturbations. Some μ-stability criteria, which depend on the range of distributed delay and the decay rate of discrete delay (not the range), are derived by using Lyapunov-Krasovski functional method. Those criteria are expressed in the form of linear matrix inequalities and they can easily be checked. Two numerical examples are provided to demonstrate the effectiveness of the obtained results. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We study an atypical nonlinear perturbation problem on the lowest three states of a harmonic oscillator. The perturbation is such that the total potential is a single-well at low values of coupling strength, turns to a double-well in the intermediate coupling range and finally becomes a triple-well at high values of the coupling strength. Proceeding via logarithmic perturbation theory, we notice that the perturbation furnishes exact results for both the energy and wave function of the second excited state but shows divergence for the first excited one. However, the ground state wave function is found to be exactly summable to the correct result with a finite energy series. Effects of varying the coupling constant, and hence the number of wells, on energies and wave functions of the concerned states are noted. Our results show further that the perturbed ground state acquires a pre-exponential factor and, strangely, an exponent same as the second excited state. The origin of such an outcome is analyzed. We also highlight the reason behind the Klauder phenomenon that tells of increased sustenance of memory effects in wave functions, when compared with the Hamiltonian, in the limit of zero coupling strength. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012 [ABSTRACT FROM AUTHOR]