Stability Conditions In Terms Research Articles

The Study of Internal Gravity Waves in the Earth’s Atmosphere by Radio Occultations: A Review

Internal gravity waves (IGWs) in the middle atmosphere are the main source of mesoscale fluctuations of wind and temperature. The parameterization of IGWs and study of their climatology is necessary for the development of global atmospheric circulation models. In this review, we focus on the application of Radio Occultation (RO) observations for the retrieval of IGW parameters. (1) The simplest approach employs the retrieved temperature profiles. It is based on the fact that IGWs are highly anisotropic structures and can be accurately retrieved by RO. The basic assumption is that all the temperature fluctuations are caused by IGWs. The smoothed background temperature profile defines the the Brunt–Väisälä frequency, which, together with the temperature fluctuations, defines the IGW specific potential energy. Many studies have derived the distribution and climatology of potential energy, which is one of the most important characteristics of IGWs. (2) More detailed analysis of the temperature profiles is based on the derivation of the temperature fluctuation spectra. For saturated IGWs, the spectra must obey the power law with an exponent of −3. Such spectra are obtained by using Wave Optical (WO) processing. (3) More advanced analysis employs space–frequency analysis. It is based on phase-sensitive techniques like cross S- or wavelet transforms in order to identify propagating IGWs. (4) Another direction is the IGW parameter estimate from separate temperature profiles applying the stability condition in terms of the Richardson number. In this framework, a necessary condition is formulated that defines whether or not the temperature fluctuations can be related to IGW events. The temperature profile retrieval involves integral transforms and filtering that constitute the observation filter. (5) A simpler filter is implemented by the analysis of the RO amplitude fluctuation spectra, based on the diffraction theory in the framework of the phase screen and weak fluctuation approximations. The two spectral parameters, the external scale and the structural characteristic, define the specific potential energy. This approach allows the derivation of the spacial and seasonal distributions of IGW activity. We conclude that the success of IGW study by RO is stimulated by a large number of RO observations and advanced techniques based on Fourier and space–time analysis, physical equations describing IGWs, and diffraction theory.

Saturated H∞ control of networked systems under stochastic transmission delays: The random sampling periods case

AbstractIn this paper, the saturated control problems of networked systems with random sampling periods and stochastic transmission delays are investigated. The main issue is to design an saturated controller such that the controlled close‐loop system is exponentially mean‐square stable with a desired performance. A matrix exponential which is different from some existing literature is used to reconstruct the discrete‐time stochastic system to an equivalent yet tractable augmented model without any additional conditional constraint. In virtue of reduced‐order confluent Vandermonde matrix approach and Kronecker product operation, the stability condition in terms of linear matrix inequality is derived and then the desired saturated controller is designed. It should be emphasized that the improved method can also be used for the stability analysis and controller design when the system matrix contains complex roots. Finally, two numerical examples and a three‐axis milling machine system are utilized to manifest the reliability and practicality of the designed strategy.

LMIs-based exponential stabilization for interval delay systems via congruence transformation: Application in chaotic Lorenz system

This paper investigates the stochastic Takagi-Sugeno (T-S) fuzzy uncertainty-dependent state feedback sampled-data control, asymptotical stability and exponential stability analysis for a class of stochastic T-S fuzzy system with measurable uncertainties, mixed interval time varying delays and Gaussian white noise. Firstly, the T-S fuzzy model and stochastic Bernoulli theory are employed to approximate the system plant. Secondly, the stochastic T-S fuzzy uncertainty-dependent state feedback sampled-data controller is designed via uncertainty-dependent parameters and the hold times series of sampled-data. Thirdly, the Bernoulli probability distribution is employed to describe the random occurrence characteristic of multipath packet dropouts. Three classes of delay-dependent stability conditions in terms of linear matrix inequalities (LMIs) are derived for the closed-loop system. The multiple integral fuzzy-basis-dependent Lyapunov functional and augmented state variable are employed to derive the delay-dependent stability conditions, then the closed-loop system is asymptotically stable and exponentially stable. The congruence transformation method and prescribed H-infinity performance functional are employed to derive the less conservative delay-dependent stability conditions, and the prescribed H-infinity performance is guaranteed. The relaxation matrix and congruence transformation method are employed to design the linear transformation equalities and congruence transformation matrices, then the controller gain matrix is determined and computation complexity of solving LMIs is reduced. Finally, the proposed method is applied in the chaotic Lorenz system to show the effectiveness and advantage of proposed method.

Expected Changes in Rainfall-Induced Landslide Activity in an Italian Archaeological Area

Cultural heritage is one of the most exceptional resources characterizing the Italian territory. Archaeological heritage, i.e., the archaeological sites with different types of archaeological artifacts, strongly contributes to enriching the national and international cultural heritage. Nevertheless, it is constantly exposed to external factors, such as natural deterioration, anthropic impact, and climate-related hazards, which may compromise its conservation. In Italy, many archaeological areas are affected by significant soil settlements that involve a large part of monuments. This paper focuses on the landslide hazard assessment of the archaeological site of Pietrabbondante (Molise region, Italy). The impact of the expected rainfall regimes, according to the EURO-CORDEX projections, on slope stability conditions were evaluated through the application of a physically based model that couples a hydraulic and a mechanical model to evaluate slope stability evolution due to pore pressure changes. Given the unavoidable lack of knowledge of the geotechnical soil properties in an archaeological heritage area, the proposed method considered the random uncertainty of soil parameters by means of a probabilistic approach in order to assess the stability conditions in terms of probability of occurrence of a landslide. The results of this study provide a reference for the safety assessment and preventive conservation of archaeological areas characterized by high cultural value.

Delay-dependent stability conditions for differential–difference equations with small commutators in a banach space

Let [Formula: see text] and [Formula: see text] be bounded operators in a Banach space. For the equation [Formula: see text] we derive sharp explicit delay-dependent exponential stability conditions via the commutator [Formula: see text]. The stability conditions in terms of the commutator enable us to construct a feedback with delay, which stabilizes a system. Gives us a possibility construct Stabilization of Systems with Retarded Feedback in a Banach Space. Our results are new even in the finite-dimensional case.

Motives of moduli spaces of bundles on curves via variation of stability and flips

AbstractWe study the rational Chow motives of certain moduli spaces of vector bundles on a smooth projective curve with additional structure (such as a parabolic structure or Higgs field). In the parabolic case, these moduli spaces depend on a choice of stability condition given by weights; our approach is to use explicit descriptions of variation of this stability condition in terms of simple birational transformations (standard flips/flops and Mukai flops) for which we understand the variation of the Chow motives. For moduli spaces of parabolic vector bundles, we describe the change in motive under wall‐crossings, and for moduli spaces of parabolic Higgs bundles, we show the motive does not change under wall‐crossings. Furthermore, we prove a motivic analogue of a classical theorem of Harder and Narasimhan relating the rational cohomology of moduli spaces of vector bundles with and without fixed determinant. For rank 2 vector bundles of odd degree, we obtain formulae for the rational Chow motives of moduli spaces of semistable vector bundles, moduli spaces of Higgs bundles and moduli spaces of parabolic (Higgs) bundles that are semistable with respect to a generic weight (all with and without fixed determinant).

Stability analysis of some neutral delay-differential equations with a frequency-domain approach

<p style='text-indent:20px;'>Two general schemes of neutral delay differential equations are considered. They represent non delayed systems with delayed, nonlinear feedback control. The stability conditions in terms of system parameters are derived using an approach based on feedback systems, namely, the Nyquist stability criterion. It is also shown that those results coincide with some already found in the literature, and others derived here, which are based on classical tools, that investigate directly the roots of characteristic equation. Finally, some examples are given to illustrate the usefulness of this approach.</p>

Sampled-Data Extremum Seeking With Constant Delay: A Time-Delay Approach

This article proposes a constructive method for sampled-data extremum seeking (ES) with square wave dithers and constant delays, by using two time-delay approaches: one to averaging and the other to sampled-data control. We consider gradient-based ES for static maps which are of quadratic forms. By transforming the ES system to the time-delay system, we have developed a stability analysis via a Lyapunov–Krasovskii method. We derive the practical stability conditions in terms of linear matrix inequalities for the resulting time-delay system. The time-delay approach offers a quantitative calculation on the upper bound of the dither and sampling periods, constant delays that the ES system is able to tolerate, as well as the ultimate bound of the extremum seeking error. This is in the presence of uncertainties of extremum value and extremum point.

Stochastic fuzzy predictive fault‐tolerant control for time‐delay nonlinear system with actuator fault under a certain probability

AbstractOwing to the characteristics of time‐delay, fault randomness, uncertainty, nonlinearity and unknown interference in industrial production processes, a stochastic fuzzy predictive fault‐tolerant control algorithm is put forward based on the traditional fault‐tolerant control algorithm. The main idea of this algorithm is to integrate actuator fault into the established Takagi‐Sugeno (T‐S) model to solve actuator fault under a certain probability for the nonlinear industrial processes with time‐varying delays by combining stochastic control theory and relevant theorems. First, the actuator fault under a certain probability is considered as a T‐S model, which can be used as a description of the fault situation in the nonlinear industrial processes. Afterwards, the augmented state space model is established through integrating state deviation and output tracking error. Second, the stochastic fuzzy predictive fault‐tolerant control law can be designed on the basis of the augmented model. Meanwhile, the actuator control mode for different faults is given. If the actuator fault is under a small probability, the control mode is switched to normal control; if the actuator fault is under a large probability, the control mode is switched to fault‐tolerant control. To this end, this control algorithm can reduce energy consumption and raw material consumption. On this basis, the designed control law can be solved by using the given stochastic stability conditions in terms of linear matrix inequality. Finally, the temperature control process of a strongly nonlinear continuous stirred tank reactor is selected as a simulation object to prove the feasibility and effectivity of this algorithm.

Event-triggered control of systems with sector-bounded nonlinearities and intermittent packet transmissions

The problem of event-triggered sampled-data control of nonlinear systems with sector-bounded nonlinearities is considered. We assume that sensors transmit their measurements to the controller over a communication channel, where the success of transmissions is defined by an i.i.d. Bernoulli process. For the analysis of the closed-loop system stability, we use the Lyapunov–Krasovskii technique. As a result, we obtain stability conditions in terms of linear matrix inequalities (LMIs), which can be used to design the appropriate triggering parameters. A global strictly positive minimum inter-event time is guaranteed to exist by design with the proposed triggering condition. A numerical example demonstrates the efficiency of the event-triggered approach in reducing the number of transmissions compared to periodic sampling, where the period is the enforced minimum time in the event-triggering condition.

Fuzzy sampled-data control for single-master multi-slave teleoperation systems with stochastic actuator faults

This article investigates the sampled-data control design for single-master multi-slave teleoperation systems with stochastic actuator faults and time-varying delays. At first, the nonlinear bilateral teleoperation systems are modeled as Takagi–Sugeno (T–S) fuzzy systems through membership functions. The decentralized sampled-data control technique is proposed with actuator faults occurring in both master and slave robots. Here, the stochastic faults satisfy certain probability conditions and the forward and backward delays between the master and slaves are time-variant and asymmetric. Next, the delay-dependent Lyapunov–Krasovskii functionals (LKFs) are constructed for the proposed fuzzy model to obtain sufficient stability conditions in terms of linear matrix inequality (LMI). Finally, the reliability and superiority of the proposed method are illustrated by numerical results.

An MPC-LQR-LPV Controller with Quadratic Stability Conditions for a Nonlinear Half-Car Active Suspension System with Electro-Hydraulic Actuators

The active suspension system of a vehicle manipulated using electro-hydraulic actuators is a challenging nonlinear control problem. In this research work, a novel Linear Parameter Varying (LPV) State-Space (SS) model with a fictional input is proposed to represent a nonlinear half-car active suspension system. Four different scheduling parameters are used to embed the nonlinearities of both the suspension and the electro hydraulic actuators to represent its nonlinear behavior. A recursive least squares (RLS) algorithm is used to predict the future behavior of the scheduling parameters along the prediction horizon. A Model Predictive Control-Linear Quadratic Regulator (MPC-LQR) is implemented as the control strategy and, to ensure stability, Quadratic Stability conditions are imposed as Linear Matrix Inequalities (LMI) constraints. Furthermore, the inclusion of attraction sets to overcome the conservative performance imposed by the Quadratic Stability conditions is included, as well as a terminal set were the switching between the MPC and the LQR controller is made. Simulations results for the half-car active suspension model over a typical road disturbance are tested to show the effectiveness of the proposed MPC-LQR-LPV controller with quadratic stability conditions in terms of comfort and road-holding.

Global exponential stability of memristor based uncertain neural networks with time-varying delays via Lagrange sense

ABSTRACT This paper addresses the global exponential stability in Lagrange sense for memristor-based neural networks (MNNs) with time-varying delays. This paper attempts to derive the delay-dependent Lagrange stability conditions in terms of linear matrix inequalities by designing a suitable Lyapunov-Krasovskii functionaland used Wirtinger inequality, Jensen-based inequality for estimating the integral inequalities. The conditions which are derived confirms the globally exponential stability in Lagrange sense for the proposed MNNs and, the detailed estimation for global exponential attractive set is also given. To show the effectiveness and applicability of the proposed criteria, two numerical examples are also provided in this paper.

Finite-region stability of 2-D singular Roesser systems with directional delays

In this paper, the problem of finite-region stability is studied for a class of two-dimensional (2-D) singular systems described by using the Roesser model with directional delays. Based on the regularity, we first decompose the underlying singular 2-D systems into fast and slow subsystems corresponding to dynamic and algebraic parts. Then, with the Lyapunov-like 2-D functional method, we construct a weighted 2-D functional candidate and utilize zero-type free matrix equations to derive delay-dependent stability conditions in terms of linear matrix inequalities (LMIs). More specifically, the derived conditions ensure that all state trajectories of the system do not exceed a prescribed threshold over a pre-specified finite region of time for any initial state sequences when energy-norms of dynamic parts do not exceed given bounds.

Stability Conditions for Remote State Estimation of Multiple Systems over Multiple Markov Fading Channels

We investigate the stability conditions for remote state estimation of multiple linear time-invariant (LTI) systems over multiple wireless time-varying communication channels. We answer the following open problem: what is the fundamental requirement on the multi-sensor-multi-channel system to guarantee the existence of a sensor scheduling policy that can stabilize the remote estimation system? We propose a novel policy construction and analytical framework and derive the necessary-and-sufficient stability condition in terms of the LTI system parameters and the channel statistics.

Asymptotically Necessary and Sufficient Quadratic Stability Conditions of T-S Fuzzy Systems Using Staircase Membership Function and Basic Inequality

Asymptotically necessary and sufficient quadratic stability conditions of Takagi-Sugeno (T-S) fuzzy systems are obtained by utilizing staircase membership functions and a basic inequality. The information of the membership functions is incorporated in the stability analysis by approximating the original continuous membership functions with staircase membership functions. The stability of the T-S fuzzy systems was investigated based on a quadratic Lyapunov function. The asymptotically necessary and sufficient stability conditions in terms of linear matrix inequalities were derived using a basic inequality. A fuzzy controller was also designed based on the stability results. The derivation process of the stability results is straightforward and easy to understand. Case studies confirmed the validity of the obtained stability results.

Prediction and Validation of Landing Stability of a Lunar Lander by a Classification Map Based on Touchdown Landing Dynamics’ Simulation Considering Soft Ground

In this paper, a method for predicting the landing stability of a lunar lander by a classification map of the landing stability is proposed, considering the soft soil characteristics and the slope angle of the lunar surface. First, the landing stability condition in terms of the safe (=stable), sliding (=unstable), and tip-over (=statically unstable) possibilities was checked by dropping a lunar lander onto flat lunar surfaces through finite-element (FE) simulation according to the slope angle, friction coefficient, and soft/rigid ground, while the vertical touchdown velocity was maintained at 3 m/s. All of the simulation results were classified by a classification map with the aid of logistic regression, a machine-learning classification algorithm. Finally, the landing stability status was efficiently predicted by Monte Carlo (MC) simulation by just referring to the classification map for 10,000 input datasets, consisting of the friction coefficient, slope angles, and rigid/soft ground. To demonstrate the performance, two virtual lunar surfaces were employed based on a 3D terrain map of the LRO mission. Then, the landing stability was validated through landing simulation of an FE model of a lunar lander requiring high computation cost. The prediction results showed excellent agreement with those of landing simulations with a negligible computational cost of around a few seconds.

Delayed stabilization of parabolic PDEs via augmented Lyapunov functionals and Legendre polynomials

We first study stabilization of heat equation with globally Lipschitz nonlinearity. We consider the point measurements with constant delay and use spatial decomposition. Inspired by recent developments in the area of ordinary differential equations (ODEs) with time-delays, for the stability analysis, we suggest an augmented Lyapunov functional depending on the state derivative that is based on Legendre polynomials. Global exponential stability conditions are derived in terms of linear matrix inequalities (LMIs) that depend on the degree N of Legendre polynomials. The stability conditions form a hierarchy of LMIs: if the LMIs hold for N, they hold for N+1. The dual observer design problem with constant delay is also formulated. We further consider stabilization of Korteweg–de Vries–Burgers (KdVB) equation using the point measurements with constant delay. Due to the third-order partial derivative in KdVB equation, the Lyapunov functionals that depend on the state derivative are not applicable here, which is different from the case of heat equation. We suggest a novel augmented Lyapunov functional depending on the state only that leads to improved regional stability conditions in terms of LMIs. Finally, numerical examples illustrate the efficiency of the method.

New relaxed stability and stabilization conditions for both discrete and differential linear repetitive processes

The paper develops new results on stability analysis and stabilization of linear repetitive processes. Repetitive processes are a distinct subclass of two-dimensional (2D) systems, whose origins are in the modeling for control of mining and metal rolling operations. The reported systems theory for them has been applied in other areas such iterative learning control, where, uniquely among 2D systems based designs, experimental validation results have been reported. This paper uses a version of the Kalman–Yakubovich–Popov Lemma to develop new less conservative conditions for stability in terms of linear matrix inequalities, with an extension to control law design. Differential and discrete dynamics are analysed in an unified manner, and supporting numerical examples are given.

Robust stability analysis and feedback control for networked control systems with additive uncertainties and signal communication delay via matrices transformation information method

The interval type-2 Takagi-Sugeno (T-S) fuzzy dynamic output feedback and H-infinity stability analysis is studied for a class of networked control systems with multiple time-varying additive uncertainties, time-varying signal communication delay and external disturbance. Firstly, the interval type-2T-S fuzzy is employed to denote the system plant. Secondly, the multiple time-varying additive uncertainties are introduced in the controller design and the state variables depending on additive uncertainties. Thirdly, the delay-dependent Lyapunov-Krasovskii functional with double integral terms is designed to derive the less conservative stability conditions in terms of linear matrix inequalities (LMIs). The characteristic of the state variables are reflected effectively by employing the controller with multiple time-varying additive uncertainties. The closed-loop system is asymptotically stable with prescribed H-infinity performance index γ by employing the matrices transformation information. The less conservative stability conditions are derived and extended into the networked control system without additive uncertainties. Finally, simulations are presented to show the effectiveness of the proposed methods.