Calculation of Lyapunov Exponents using Nonstandard Finite Difference Discretization Scheme: A Case Study

Stability analysis of discrete-time systems with arbitrary delay kernels based on kernel-related summation inequality and model transformation

Practical applications of Lyapunov's direct method to transient stability analyses of multimachine power systems have been obstructed by the well-known conservative nature and the computational difficulty accompanying the usual critical value of Lyapunov function. These problems have been solved in this paper by introducing a new critical value for the first swing stability, and by developing a efficient method of calculating it as well as one of taking account of transfer conductances. These methods have been applied to a transient stability analysis of a 10-machine power system, and yielded results of practical significance.

On construction of non-smooth lyapunov functions for non-smooth systems

Stability and steady state analysis of control and safety systems of Nuclear Power Plants

Power systems are being operated close to their voltage security limit which makes their reliable operation more challenging. Voltage stability has been a major problem faced by utilities now a days. Many blackout have been reported around the world related to voltage instability problem. Many voltage stability analysis methods have been presented up till now. Here artificial neural network based approach for voltage stability analysis of power system is presented. Voltage stability analysis of power system has been done in terms of voltage stability margin. Voltage stability margin is calculated by estimating distance from current operating point to maximum voltage stability point according to loading parameter. Principal Component Analysis is an efficient feature selection method used here to find few input variables required to estimate voltage stability margin with sufficient accuracy and execution speed. Major drawback of previously published work is they need to train new neural network whenever change in system topology occur which is very time consuming process. Therefor in this paper single ANN has been prepared for estimating VSM for several system configuration. Feed forward neural network and radial basis function neural network have been used for voltage stability analysis of power system. The final result indicate that proposed method provide an efficient and compact ANN model for different system configuration as well as base case operating condition with lowest possible input required.

This study aims to examine the nonlinear features of electromagnetic pulses that propagate obliquely to an external magnetic field within the nonlinear Zakharov Kuznetsov modified equal-width equation. This research will contribute to understanding the complicated dynamical nature of the presented model that implies different areas of research. Our objective is to show the traveling wave solution and stability analysis of the dynamic system. A modified Sardar sub equation technique is applied to find the traveling wave solution of the underlying problem. The traveling wave solution is obtained in a broad variety including solitons, kinks, periodic solutions, rational solutions, and many others. The dynamical analysis starts with phase portraits which provides information to the qualitative dynamics of the system and its stability features. The sensitivity analysis will examine the influence of parameters on the model to provide insights that demonstrate the effectiveness of the model and to examine the behavior of the dynamical system under different initial conditions. We also investigate the chaotic dynamics to identify the stability and categorize periodic, quasi-periodic, and chaotic dynamics of the perturbed dynamical system. These analyses demonstrate the potential application and enhance the underlying mechanics in the field of optical and nonlinear physics. This dynamical analysis improves understanding of nonlinear models and develops efficient mechanisms to manage the complex nonlinear model. Furthermore, Poincare map and Lyapunov exponent are used to find qualitative behavior and visualize the phase space to illustrate the various dynamical regimes. These contributions enhance the improvement in the field of optical soliton and help to analyze the complex dynamical system in the field of engineering and mathematical physics.

Enhanced robust stability analysis of large hydraulic control systems via a bifurcation-based procedure

Lyapunov's direct method has been applied extensively to the stability analysis of nonlinear systems. The method enables one to directly judge stability without solving the nonlinear differential equations representing motor involved. In the paper, the effect of important parameters on trasient stability of a three-phase reluctance motors have been assessed from the data obtained for load and applied voltage changes by applying the Lyapunov's direct method.

This paper mainly investigates the state constrained switched system with fully unstable subsystems. By limiting the state in a unit hypercube, a sufficient condition is derived to ensure the stability of such systems via a time-dependent strategy. The main idea is to use positive switching behavior to compensate state divergence caused by unstable states and setting a different ascend rate when state constraints occur or not. In order to make the conditions computable for a continuous-time switched systems with state constraints, the discretized Lyapunov Function method is applied, then a numerical example is given to show the practicability of the proposed method.

In practice, there exist such controlled systems in which some states are often not available, not measurable or too expensive to measure. For such systems, impulsive control inputs may be exerted on the available partial states so as to stabilize the underlying systems. This paper is concerned with analyzing the stability of a class of nonlinear time-delay systems with partial states subject to impulsive inputs. The main idea is that the entire impulsively controlled system can be viewed as a hybrid one that is composed of a stable continuous subsystem and a stable impulsive subsystem. Then the analysis technique based on the new time-varying weighted Lyapunov functional/function introduced is utilized to derive sufficient conditions for exponential stability of such systems. As an illustration of the utility of the new stability criteria, the batch reactor system with the try-once-discard protocol is examined.

The use of active vibration control may induce a delay leading to detrimental degradation of the performance of active vibration control. This is particularly true in the case of mechanical systems subjected to friction-induced vibration and noise for which such time-delays can lead to the appearance of undesirable instability. Furthermore, conducting a stability analysis of time-delay systems and estimation of the critical time delay are challenging, due to the infinite nature of the characteristic (quasi) polynomial of the associated closed-loop system, having an infinite number of roots.The objective of this paper is to discuss a strategy for the estimation of the critical time delay for the problem of Friction-Induced Vibration and noisE (FIVE). To achieve such an objective, the prediction of the stability analysis of time delay systems and the estimation of the associated critical time delay are first performed by applying the frequency sweep test and the eigenvalue problem approximation using the Taylor series expansion of the delayed term. In a second time, a mixed approach is proposed to predict effectively the real critical time delay of autonomous controlled systems subjected to friction-induced vibration. The efficiency of the proposed approach is illustrated by numerical examples for the prediction of self-sustaining vibrations of a phenomenological model with two degrees of freedom for which it is possible to provide a clear understanding and illustration of the phenomena involved and observed.

In this paper, the dynamic stability analysis of an elastic rod subjected to conservative and nonconservative forces by using the integral equation method is presented. The stability analysis of multiple-parameter elastic system is taken consideration with two types damping terms, which are the internal and the exteral damping effects. The numerical method derived from the boundary integral equation in the sub-domain, which was proposed for dynamic stability analysis of oneparameter system subjected to nonconservative force, is applied to the analysis of multiple-parameter systems. The models in numerical examples are cantilever-type elastic rods under the combined action of these forces. The obtained numerical results proved the effectiveness of our method and showed mechanical characteristics for these multiple-parameter systems.

This paper proposes a novel generalized integral inequality based on free matrices and applies it to stability analysis of time-varying delay systems. The proposed integral inequality estimates the upper bound of the augmented quadratic term of the state and its derivative term by utilizing not only the single integral term but also the higher-order multiple integral terms. The proposed integral inequality includes several well-known integral inequalities as special cases. For the stability analysis of time-varying delay systems, a new Lyapunov-Krasovskii functional is constructed by including the double integral term with the augmented vector of the state and its derivative to utilize the proposed integral inequality when estimating the derivative of the Lyapunov-Krasovskii functional. Furthermore, to fully exploit the information on the time-varying delay, this paper divides the interval of the double integral term into two parts. Two numerical examples show that the results of the proposed method outperform those of the existing methods.

Uncertainty of parameters in control systems was described by interval variables, and some idea of the non-probabilistic reliability method that we proposed in previous papers was used for stability analysis and synthesis of uncertain systems. A new method, called robust reliability method, was presented for quadratic stability analysis and robust stabilization of dynamic systems with interval parameters. In the method, the performance function for robust reliability calculation was established by criterion of quadratic stability, and a solving method in the form of optimization for robust reliability was presented. The proposed stabilization method can take both the required energy supply for control and the control robustness into account. This makes the reasonable strategy of compromising between the control cost and system reliability become possible. By the method, robust reliability measure of the stability degree of uncertain control systems can be provided, and the maximum allowable ranges of the basic parameters can be obtained. The presented method is based on the linear matrix inequality (LMI) approach, and is convenient to implement Three numerical examples were provided to illustrate the validity and efficiency of the presented method.

The stability analysis of time-delay systems is a tough task even in the linear case, especially when time-varying delays are considered. In recent years, for the class of positive delay systems, a number of insightful works appeared in the literature, highlighting their peculiar stability properties, which lead to simple and easy to check necessary and sufficient conditions for the delay-independent stability. This fact poses the question whether some results that hold for positive systems can be exported to arbitrary systems. In some recent papers we gave an answer to this question by extending to the time-delay setting the Internally Positive Representation technique, a method that allows to systematically construct positive representations of arbitrary systems. In this work, after a survey on recent stability results for positive delay systems, an overview of the Internally Positive Representation technique and of its implications on the stability analysis of arbitrary systems is reported. Three classes of linear systems are considered: delay differential, delay difference, and coupled delay differential-difference systems.