Inequality Conditions Research Articles

Existence of C 1 -Positive Solutions for a Class of Second-Order Impulsive Differential Equations

In this study, under some inequality conditions, necessary and sufficient conditions, using fixed-point theorem in cones, are established for the existence of C 1 -positive solutions for a class of second-order impulsive differential equations. Two examples are given in the last section to illustrate the abstract results.

Event‐triggered leader‐following consensus for a class of nonlinear multiagent systems with time‐varying delay

AbstractThis article studies the consensus problem for discrete‐time nonlinear multiagent systems with time delay. Based on an asynchronous event‐triggered mechanism where local information of a communication graph is involved, a distributed consensus protocol is proposed to reduce the network communication congestion for achieving state consensus for multiagent systems with nonlinear perturbations. To avoid complications involving data fusion, this distributed consensus protocol allows every agent to broadcast its state at its own triggering condition instead of using continuous updates and without continuous monitoring of the triggering condition. To save the energy consumption involved in a consensus protocol, the proposed event‐triggering guaranteed cost is investigated in this article for multiagent systems. We select an agent as a leader that is constrained by its neighbors and controlled by the proposed protocol as other agents. It has been theoretically demonstrated that the consensus problem of multiagent systems with nonlinear perturbation and time delays can be achieved if the control gains and the triggering parameters are appropriately selected. Sufficient conditions are given to guarantee that the agents achieve consensus. Moreover, the gain matrix and triggering parameters of the proposed protocol are cast into matrix inequalities conditions. A simulation example is given to illustrate the effectiveness of the theoretical results.

Resilient active seismic response control of structural systems

This paper proposes a dissipative resilient observer and controller (DROC) design for a network controlled system (NCS) that handles faults, implementation errors, or cyberattacks that can be modeled as bounded controller or observer gain perturbations. It presents linear matrix inequality (LMI) conditions for the robust stability of the system in the presence of bounded perturbations in the observer and controller. Furthermore, a new LMI-based time-delay control (TDC) algorithm that mitigates the effects of perturbations due to time-delays in the NCS is introduced. The robust methodology is applied to active control of a scaled model of a structural system equipped with an active mass driver system. The results demonstrate that the proposed methodology is robust and ensures stable system response due to various types of earthquake base excitations.

Structural Racism as an Environmental Justice Issue: A Multilevel Analysis of the State Racism Index and Environmental Health Risk from Air Toxics

Communities of color and poor neighborhoods are disproportionately exposed to more air pollution—a pattern known as environmental injustices. Environmental injustices increase susceptibility to negative health outcomes among residents in affected communities. The structural mechanisms distributing environmental injustices in the USA are understudied. Bridging the literatures on the social determinants of health and environmental justice highlights the importance of the environmental conditions for health inequalities and sheds light on the institutional mechanisms driving environmental health inequalities. Employing a critical quantitative methods approach, we use data from an innovative state racism index to argue that systematic racialized inequalities in areas from housing to employment increase outdoor airborne environmental health risks in neighborhoods. Results of a multilevel analysis in over 65,000 census tracts demonstrate that tracts in states with higher levels of state-level Black–white gaps report greater environmental health risk exposure to outdoor air pollution. The state racism index explains four-to-ten percent of county- and state-level variation in carcinogenic risk and noncarcinogenic respiratory system risks from outdoor air toxics. The findings suggest that the disproportional exposure across communities is tied to systematic inequalities in environmental regulation and other structural elements such as housing and incarceration. Structural racism is an environmental justice issue.

The Effect of Human Capital Inequality on Income Inequality: Evidence from Indonesia

Education inequality in Indonesia tends to experience a downward trend which indicates that the education distribution is more equally distributed from year to year. this phenomenon should lead to a reduction in income inequality. However, income inequality in Indonesia has increased compared to 9 years ago. This study intends to look at the human capital inequality condition in provinces in Indonesia and analyze the effect of human capital inequality on income inequality. The Gini coefficient concept is used to measure human capital inequality and income inequality. The annual panel data covered 34 provinces in Indonesia from 2015 – 2019. The analytical methods used dynamic panel data regression using the Generalized Method of Moment (GMM) Arellano-Bond approach. The results indicate income inequality with a lag of 1 year, literacy rate, and trade openness have a negative and significant effect on income inequality. Furthermore, the human capital inequality and the average years of schooling have a positive and significant effect on income inequality. So, to reduce income inequality, policymakers are advised to minimize human capital inequality, especially in the education sector by paying attention to conditions in priority provinces.

A importância da inclusão social das crianças e adultos menos favorecidos à educação à distância

The aim is to discuss the importance of the social inclusion of children and adults belonging to less favored classes in distance education. In order to do so, it highlights the main characteristics observed in distance education, demonstrating through studies and analysis how this teaching modality has been growing in Brazil and showing the positive points in promoting the integration between technology and educational routines. In the process of elaboration of the work, a bibliographical research was carried out to present the main concepts, analyzes and observations regarding distance education and its application, highlighting that through this educational modality some people manage to promote their school development, although still It is necessary to look for alternatives so that needy students have access to distance education, since a large part of the most impoverished layer of the population does not have a computer or internet, which puts them in a condition of inequality in relation to other students who have access to the ICTs.

Una aproximación a los feminismos situados en los <<márgenes>>. Sus propuestas sociales y políticas desde el activismo digital

Technology is undoubtedly part of our lives, and the pandemic caused by COVID-19 has accelerated the so-called digital transition, causing changes in all social, economic, and political structures. One element that has followed this trend has been activism, which, although it was already taking place in the digital realm, has enhanced its transformation. Because of the globalization and digitization of the world, societies are becoming increasingly plural, diverse, and heterogeneous. Following the principles of the Culture of Peace, it is necessary to welcome and work by, for, and with such diversity; to analyze the mechanisms through which such diversity is, according to certain circumstances, in conditions of inequality and to investigate the strategies of response to such inequalities. Thus, this research proposes to analyze (e)activism as a form of political participation focusing on the case of the feminist struggle from the perspective of several feminist women "from the margins" (Suárez and Hernández, 2008) and having as objectives to analyze the (e)activism of these feminisms in Spain, their social and political proposals and the role played by the digital in its dissemination. To respond to these objectives and considering the nature of the object of study, a digital ethnography is proposed as a methodology, integrating bibliographic analysis, virtual non-participant observation, and online interviews. Finally, the results of this study indicate that the discourses of the interviewees point to the importance of recognizing cultural otherness, and that it is necessary not so much to integrate diversity as to decolonize society and its individuals. As feminists, they are committed to the visibility of gender-specific issues from an intersectional approach. As (e)activists, they transform these demands into content and share them through online media, without ignoring the importance of offline activism, transmitting their speeches publicly, promoting solidarity ties, using art as a tool, and raising awareness in Spanish society. &nbsp

Asymptotics for some discretizations of dynamical systems, application to second order systems with non-local nonlinearities

<p style='text-indent:20px;'>In the present paper we study the asymptotic behavior of discretized finite dimensional dynamical systems. We prove that under some discrete angle condition and under a Lojasiewicz's inequality condition, the solutions to an implicit scheme converge to equilibrium points. We also present some numerical simulations suggesting that our results may be extended under weaker assumptions or to infinite dimensional dynamical systems.</p>

Pandemic disruptions to access to higher education in South Africa: A dream deferred?

The COVID-19 pandemic and the shift to emergency remote teaching (ERT) and online learning highlighted issues of social justice, pedagogical inclusion and epistemic access in higher education. The research underlying this article analyses the complexities of access to learning and the effects of the shift to ERT and online learning on the social justice agenda in South Africa, using the case study of the University of Johannesburg. The article uses the conceptual frameworks of epistemic access, equity and inclusive pedagogy from the theories of Fraser (2008), Mbembe (2016) and Mgqwashu (2016). Pedagogic continuity and inclusion (Motala and Menon 2020; Menon and Motala 2021), hard-won by many institutions during the pandemic, will need to be sustained and secured as the world adapts to a “new normal” in higher education and other spheres of life. Czerniewicz et al. (2020, 957) refer to the maxim “Anytime, anyplace, anywhere” characterising ERT as a “brutal underestimation of the complexities and entanglement of different inequalities and structural arrangements”. Fataar (2020), Czerniewicz et al. (2020) and Hodges et al. (2020) advocate an alternative pedagogy that is “trauma-informed” and offers parity with the pedagogies that prevailed pre-pandemic. The article concludes that the pre-existing conditions of deep inequality and inequities, and a highly differentiated higher education system with uneven pedagogical practices, were exacerbated by the pandemic. While we acknowledge the achievement of avoiding the loss of the academic year during the pandemic, we argue that it is important to learn lessons from the initial implementation of ERT and the fractures that it highlights in higher education. Heading into an uncertain future, the sector needs explicit equity-driven approaches to ensure pedagogical inclusion beyond physical and epistemic access.

Equivalent conditions of optimal half discrete Hilbert type multiple integral inequalities with quasi homogeneous kernel and applications

Equivalent conditions of optimal half discrete Hilbert type multiple integral inequalities with quasi homogeneous kernel and applications

АНАЛІЗ ПРОЦЕСУ ГАЛЬМУВАННЯ КОЛІСНИХ ТРАНСПОРТНИХ ЗАСОБІВ В УМОВАХ БОРТОВОЇ НЕРІВНОСТІ ГАЛЬМІВНИХ МОМЕНТІВ

The article is devoted to the study of the dynamics of curvilinear motion and course stability of wheeled vehicles during braking in conditions of onboard uneven braking torques. The object of the study – wheeled vehicle, the braking of which is investigated on dry, wet and slippery roads. 192 The purpose of the work is to develop methods of modeling and analysis of the braking process of the wheeled vehicle in the conditions of onboard inequality of braking moments. Research method – mathematical and computer modeling of a dynamic system. A mathematical model is proposed, which allows to investigate the occurrence of curvilinear motion (skid) of wheeled vehicle during braking and to analyze how the inequality of braking moments on the left and right wheels of wheeled vehicle affects the parameters of its movement. During braking, significant longitudinal and transverse reactions occur in the contact of the wheels with the road, which cause significant slippage of the wheels in the appropriate directions. Therefore, when determining the transverse reaction that occurs in the contact of wheels with the road, preference in the mathematical model is given not to the classical theory of wheel deflection, but to the concept of the common nature and identical patterns of interaction of the wheel with the road in both longitudinal and transverse directions. Within the framework of the mentioned concept, quantitative research has clarified the physical processes that occur when the brake wheel interacts with the road. The article investigates the influence of the onboard inequality of braking moments on the course angle during braking of a wheeled vehicle. Studies have identified the causes of the variable by the sign and the oscillating nature of the change in time of the course angle of the vehicle during braking, which complicates the driver to carry out the driving process. The results obtained in the article actualize before the designers of wheeled vehicles the question of increasing the stability of the characteristics of the brake mechanisms and the widespread use of automatic gap regulators in the friction pairs of brakes. Predictive assumptions about the development of the object of study – the development of databases to clarify the regulatory documents on the allowable values of on-board inequality of braking torques for different categories of wheeled vehicles. KEY WORDS: WHEELED VEHICLES, BRAKING PROCESS, MATHEMATICAL MODEL, COMPUTER SIMULATION, COURSE STABILITY

An equivalent property of a Hilbert-type integral inequality and its applications

Making use of complex analytic techniques as well as methods involving weight functions, we study a few equivalent conditions of a Hilbert-type integral inequality with nonhomogeneous kernel and parameters. In the form of applications we deduce a few equivalent conditions of a Hilbert-type integral inequality with homogeneous kernel, and we additionally consider operator expressions.

Constructive method for boundary control of stochastic 1D parabolic PDEs

Recently, qualitative methods for finite-dimensional boundary state-feedback control were introduced for stochastic 1D parabolic PDEs. In this paper, we present constructive and efficient design conditions for state-feedback control of stochastic 1D heat equations driven by a nonlinear multiplicative noise. We consider the Neumann actuation and apply modal decomposition with either trigonometric or polynomial dynamic extension. The controller design employs a finite number of comparatively unstable modes. We provide mean-square L2 stability analysis of the full-order closed-loop system, where we employ Itô’s formula, leading to linear matrix inequality (LMI) conditions for finding the controller gain and as large as possible noise intensity for the mean-square stabilizability. We prove that the LMIs are always feasible for small enough noise intensity. We further show that in the case of linear multiplicative noise, the system is stabilizable for noise intensities that guarantee the stabilizability of the stochastic finite-dimensional part of the closed-loop system. Numerical simulations illustrate the efficiency of our method.

Sliding mode observer based control for T-S fuzzy descriptor systems

<p style='text-indent:20px;'>In this paper, the problem of sliding mode observer (SMO) based sliding mode control (SMC) for nonlinear descriptor delay systems is studied. First, based on the T-S fuzzy dynamic modeling technique, the nonlinear descriptor system is transformed into a combination of local linear models. Then, a integral-type sliding surface (ITSS) based SMO is constructed for the error system. In the sequel, sufficient linear matrix inequality (LMI) conditions are established to ensure the admissibility of the sliding motions and obtain the observer gain matrix. Furthermore, two novel SMC laws are developed to ensure the reachability conditions and stabilize the descriptor systems. Finally, simulations are provided to show the effectiveness of the method.</p>

Preinvexity of $ n $-dimensional fuzzy number-valued functions: characterization, variational inequality and optimization problems

<abstract><p>In this paper, the preinvexity of <italic>n</italic>-dimensional fuzzy number-valued functions are defined and discussed by means of the partial order relation in <italic>n</italic>-dimensional fuzzy number space which including preinvexity, weak preinvexity, strict preinvexity, weakly strict preinvexity, prequasiinvexity, weak prequasiinvexity, strict prequasiinvexity, weakly strict prequasiinvexity, and so on. In addition, their interrelations of the preinvexity of <italic>n</italic>-dimensional fuzzy number-valued functions are discussed, and some counterexamples are given. Furthermore, the two-parameter optimization problem, $ n $-dimensional fuzzy variational-like inequality and optimality conditions related to $ n $-dimensional preinvex fuzzy number-valued functions are discussed.</p></abstract>

Design of Observer-Structured H∞ Flight Controllers Converted from Unstructured Conventional H∞ Flight Controllers

We address the conversion problem from a priori designed unstructured Linear Time-Invariant (LTI) controllers to observer-structured LTI controllers, whose structure is similar to but is not exactly the same as the so-called “Luenberger observer-based controllers”, for Linear Parameter-Varying (LPV) or LTI Parameter-Dependent (LTIPD) plant systems. For this problem, we propose a method by designing appropriate state transformation matrices which minimize the errors between plant systems’ states and transformed controllers’ states for external inputs via parametrically multi-affine Linear Matrix Inequality (LMI) conditions. The proposed method embeds existing LTI controllers with the ability of observers while their control performance is unchanged. We introduce a numerical example and illustrate the usefulness of our method by embedding observer property to an a priori designed H∞ flight controller.

LMI-Based Observer Design for Non-Globally Lipschitz Systems Using Kirszbraun–Valentine Extension Theorem

This paper deals with observer design for a class of nonlinear systems. The paper makes two notable contributions. First, we propose a solution to design an observer for systems without global Lipschitz conditions by extending the nonlinearities to globally Lipschitz functions. Secondly, we provide a novel Linear Matrix Inequality (LMI) condition ensuring asymptotic convergence of the observer. The extension of the nonlinearities is achieved by exploiting old mathematical tools on Kirszbraun-Valentine Lipschitz extensions. Once the structure of the observer, based on the extended functions, is well-posed, we propose a new LMI technique, which is more general and more convenient than those existing in the literature.

Robust Structural Stability, Stability Margins, and Maximum Uncertainty Amplification for 2D Uncertain Systems via Structured Lyapunov Functions and Matrix Annihilators

This paper considers 2D uncertain systems with homogeneous or mixed dynamics, and addresses three problems: establishing robust structural stability, computing robust structural stability margins, and determining the maximum uncertainty amplification that preserves robust structural stability. Two sufficient linear matrix inequality (LMI) conditions are proposed for establishing robust structural stability obtained by introducing an equivalent closed-loop complex system and by searching for real or complex structured Lyapunov functions and matrix annihilators parameterized by the uncertainties and auxiliary quantities. Moreover, it is shown that lower bounds of the introduced robust structural stability margins and maximum uncertainty amplification can be obtained by solving quasi-convex optimization problems under some restrictions on the sought Lyapunov functions or on the set of uncertainties. Lastly, the nonconservatism of the proposed results is analyzed, showing that the proposed LMI condition based on the use of complex Lyapunov functions is not only sufficient but also necessary under some assumptions.

Adaptive Optimal Multi-Surface Back-Stepping Sliding Mode Control Design for the Takagi-Sugeno Fuzzy Model of Uncertain Nonlinear System With External Disturbance

This paper proposes a novel scheme of the multi-objective robust control design for a class of uncertain nonlinear systems in strict-feedback-form based on Takagi–Sugeno fuzzy model (TSFM). The nonlinear system contains both the matched and the unmatched uncertainties and also subjected to the external disturbances. The TSFM provides the generalization of the linear systems concepts to the nonlinear systems field in a convex framework. First, a new sliding surface is defined using a convex combination of the surfaces which are defined for each fuzzy rule consequence local linear subsystems. Then, their gains are designed optimally via a generalized eigenvalue problem (GEVP). Also, the upper-bounds of the matched and unmatched uncertainties are estimated using the adaptive update laws. The multi-objective control aims not only to satisfy the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{2}$ </tex-math></inline-formula> -optimization performance, but also, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> -stability region is formulated to improve the transient response performance. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{2}$ </tex-math></inline-formula> -optimization characterization and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> -stability design conditions are derived in terms of new linear matrix inequalities (LMIs) conditions. Finally, the effectiveness of the proposed approach is demonstrated by considering a comparative practical example.

An LMI Approach for Stability Analysis and Output-Feedback Stabilization of Discrete-Time Lur’e Systems Using Zames-Falb Multipliers

This letter investigates the problem of stability analysis and output-feedback stabilization of discrete-time Lur'e systems where the nonlinearity is odd and slope bounded. Using the linear matrix inequality (LMI) conditions from the literature to handle the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm and positive realness constraints, an iterative algorithm based on LMIs is constructed to assess stability through the existence of a Zames-Falb multiplier of any given order based on independent positive definite matrices for the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm and positive realness. More important, the method can also deal with output-feedback stabilization. Numerical examples illustrate the performance of the proposed approach when compared with other methods.