Stability Problem Research Articles

Sampled-data controllers and observer-design for uncertain semilinear systems with positivity constraints

This paper deals with the problem of positive stabilization of a class of uncertain semilinear diffusion systems using sampled-data controllers. The conditions for the existence of such controllers are obtained through certain inequalities. By solving these inequalities, we determine upper bounds for the sampling intervals that guarantee exponential stability, as well as the corresponding decay rates. Furthermore, the design of a positive observer for systems with discrete measurements is studied. The stability of the estimation error is ensured through the same LMIs. Numerical simulations are presented to illustrate the effectiveness of the proposed approach.

Efficient hole extraction by doped-polyaniline/graphene oxide in lead-free perovskite solar cell: a computational study

Abstract The intriguing behavior of doped polyanilinine/graphene oxide (PANI/GO) offers a solution to the pivotal problem of device stability against moisture in perovskite solar cell (PSC). Tunable bandgap formation of doped PANI/GO with an absorber layer allows effective flexibility for charge carrier conduction and reduced series resistance further boosting the cell performance. Herein, the L9 Orthogonal Array (OA) Taguchi-based grey relational analysis (GRA) optimization was introduced to intensify the key output responses. Furthermore, this work also delved into incorporating a Pb-free absorber perovskite layer, formamidinium tin triiodide (FASnI3), and concomitantly eluding the environmentally hazardous substance. The numerical optimization supported by statistical analysis is based on experimental data to attain the utmost peak cell efficiency. Taguchi’s L9 OA-based GRA predictive modeling recorded over one-fold enhancement over experimental results, reaching as high as 20.28% power conversion efficiency (PCE). Despite that, the PCE of the structures is severely affected by interface defects at the electron transport layer/absorber (ETL/Abs) vicinity, which is almost zero at merely 1 × 1014 cm−2, manifesting that control measures need to be taken into account. This work deduces the feasibility of ETL/Abs stack structure in replacing the conventional Pb-based perovskite absorber layer, while maximizing the potential use of doped PANI/GO as a hole transport layer (HTL).

The Overview for the Stability Improvement Strategy of LIBS Spectrum and Analysis Model: From Physics System to Analysis Method.

Laser-induced breakdown spectroscopy (LIBS) technology has been widely used in many fields including industrial production, space exploration, medical analysis, environmental pollution detection, etc. However, the stability problem of LIBS is one of the core problems for its further development. Solutions in the LIBS field in recent decades were summarized and classified from the physical mechanism and analysis method. In particular, the processing methods based on the features of the plasma image and reconstructed image were analyzed and expounded. At the physical mechanism level, the system improvement strategy, environmental modulation strategy, and sample pretreatment improvement strategy were summarized and classified as a pre-improvement strategy. At the analysis method level, two kinds of correction strategies were concluded according to the difference between the feature mediums of the plasma spectrum and image, which were classified as a later improvement strategy. Strategies and methods were discussed in detail, which can provide a basic architecture and reference for the research of LIBS stability improvement. Moreover, the potential developing trend for this topic was proposed.

Improving the Thermal Stability of Indium Oxide n-Type Field-Effect Transistors by Enhancing Crystallinity through Ultrahigh-Temperature Rapid Thermal Annealing.

Ultrathin indium oxide films show great potential as channel materials of complementary metal oxide semiconductor back-end-of-line transistors due to their high carrier mobility, smooth surface, and low leakage current. However, it has severe thermal stability problems (unstable and negative threshold voltage shifts at high temperatures). In this paper, we clarified how the improved crystallinity of indium oxide by using ultrahigh-temperature rapid thermal O2 annealing could reduce donor-like defects and suppress thermal-induced defects, drastically enhancing thermal stability. Not only does more crystalline indium oxide depict the high stability of threshold voltage in stringent high-temperature test environments and under positive bias, but it also shows much less degradation under forming gas annealing than as-deposited transistors. Furthermore, we also successfully solved the channel length-dependent threshold voltage problem, which is often observed in oxide transistors, by suppressing defects induced by the metal deposition process and metal doping.

Design of a Finite-Time Bounded Tracking Controller for Time-Delay Fractional-Order Systems Based on Output Feedback

This paper focuses on a class of fractional-order systems with state delays and studies the design problem of the finite-time bounded tracking controller. The error system method in preview control theory is first used. By taking fractional-order derivatives of the state equations and error signals, a fractional-order error system is constructed. This transforms the tracking problem of the original system into an input–output finite=time stability problem of the error system. Based on the output equation of the original system and the error signal, an output equation for the error system is constructed, and a memory-based output feedback controller is designed by means of this equation. Using the input–output finite-time stability theory and linear matrix inequality (LMI) techniques, the output feedback gain matrix of the error system is derived by constructing a fractional-order Lyapunov–Krasovskii function. Then, a fractional-order integral of the input to the error system is performed to derive a finite-time bounded tracking controller for the original system. Finally, numerical simulations demonstrate the effectiveness of the proposed method.

Global output feedback stabilization of stochastic uncertain nonlinear systems with large constant delays

This paper studies the problem of output feedback stabilization for a class of stochastic uncertain nonlinear systems with large constant delays in state and input. For stochastic nonlinear systems, the maximal open sector Δ of output function is given. As long as output function belongs to any closed sector included in Δ, by constructing a reduced-order observer and C 2 Lyapunov–Krasovskii functional and using the homogeneous domination method, an output feedback controller can be developed to guarantee the closed-loop system globally asymptotically stable in probability.

Highly stable nickel metal-modified black phosphorus-based photodetectors with enhanced magnetic field-assisted photoresponse

The unique physicochemical properties of black phosphorus endow it with great potential for application in the field of photodetection, but its stability problem has been hindering its further development.

Data-driven stabilization of switched and constrained linear systems

We consider the design of state feedback control laws for both the switching signal and the continuous input of an unknown switched linear system, given past noisy input-state trajectories measurements. Based on Lyapunov–Metzler inequalities and on a matrix S-lemma, we derive data-dependent bilinear programs, whose solution directly returns a provably stabilizing controller and ensures H2 or H∞ performance. We further present relaxations that considerably reduce the computational cost, still without requiring stabilizability of any of the switching modes. Finally, we showcase the flexibility of our approach on the constrained stabilization problem for an unknown perturbed linear system. We validate our theoretical findings numerically, demonstrating the favorable trade-off between conservatism and tractability achieved by the proposed relaxations.

The stabilization problem for a class of discrete-time semi-Markov jump singular systems

This paper studies the stabilization problem for a class of discrete-time semi-Markov jump singular systems with mode-dependent singular matrix. Since our model is mode-dependent singular matrix, the previous methods are unable to achieve the stability. To overcome this difficulty, the novel and less conservative stability conditions with the original system coefficient matrices are constructed by developing new theories and methods. Based on the above conditions, the linear matrix inequality (LMI) based stabilizing controller design method is proposed.

Semi-global stabilization of parabolic PDE–ODE systems with input saturation

This paper addresses the semi-global stabilization problem of parabolic PDE–ODE systems with input saturation. Two low-gain controllers are proposed for two types of systems. It is shown that the proposed controllers can solve the semi-global stabilization problem of the concerned parabolic PDE–ODE systems with input saturation. Distributed-diffusion, counter-convection and Robin boundary condition are simultaneously considered. Moreover, the controllability of PDE–ODE systems with input saturation is discussed. It is shown that semi-global stabilization is impossible if the open-loop ODE system is exponentially unstable, which is another distinctive contribution of this work. Two illustrative examples are given to show the effectiveness of our proposed low-gain controllers.

Stability on 3D Boussinesq system with mixed partial dissipation

Abstract In the article, we are concerned with the three-dimensional anisotropic Boussinesq equations with the velocity dissipation in x 2 {x}_{2} and x 3 {x}_{3} directions and the thermal diffusion in only x 3 {x}_{3} direction. When the spatial domain is the whole space R 3 {{\mathbb{R}}}^{3} , the global well-posedness and stability problem for the partially dissipated Boussinesq system remain the extremely challenging open problems. Attention here focuses on the periodic domain Ω = R × T 2 \Omega ={\mathbb{R}}\times {{\mathbb{T}}}^{2} . We aim at establishing the stability for the problem of perturbations near hydrostatic equilibrium and the large-time behavior of the perturbed solution. We first obtain the global existence of some symmetric fluids in H 2 ( Ω ) {H}^{2}\left(\Omega ) for small initial data. Then the exponential decay rates for the oscillations u ˜ \widetilde{u} and θ \theta in H 1 ( Ω ) {H}^{1}\left(\Omega ) and the homogeneous Sobolev space H v 2 ˙ ( Ω ) \dot{{H}_{v}^{2}}\left(\Omega ) are also shown. The proof is based on a key observation that we can decompose the velocity u u into the average u ¯ \overline{u} on T 2 {{\mathbb{T}}}^{2} and the corresponding oscillation u ˜ \widetilde{u} . This enables us to establish the strong Poincaré-type inequalities on u ˜ \widetilde{u} , u 3 , θ {u}_{3},\theta and some anisotropic inequalities, which ensure the establishment of the closed priori estimates. In addition, we also prove the oscillations in one direction u ˜ ( 2 ) , u ˜ ( 3 ) {\widetilde{u}}^{\left(2)},{\widetilde{u}}^{\left(3)} in H 1 ( Ω ) {H}^{1}\left(\Omega ) decay to zero exponentially.

Hierarchical Sliding Mode Control Design for Stabilization of Underactuated Wheeled Acrobot System

This paper presents the hierarchical sliding mode control (HSMC)--based stabilization problem of the wheeled Acrobot (WAcrobot) system, which combines an actuated wheel that rolls in the horizontal plane with an Acrobot consisting of two inverted pendulum links. These links are driven by an actuator at the second joint and freely rotate in a vertical plane. The stabilization problem of the WAcrobot, previously addressed using switch-based controllers in many studies, is solved in this work by designing a single-stage controller without requiring switching steps or time. The design approach comprises two parts. First, the system is reduced to a cascaded nonlinear model in finite time using the inherent dynamic coupling relationship. Second, a two-loop control scheme is employed: the outer loop ensures that the actuated state variables track the desired response, while the inner loop forces them to exhibit an asymptotically stable nature. After the desired design of both loops, the asymptotic stability of the overall dynamics is achieved. Finally, the theoretical analysis is validated using MATLAB. Simulation results demonstrate that the proposed controller effectively stabilizes the WAcrobot system at the equilibrium points.

Periodic sampled-data-based dynamic event-triggered consensus of linear multiagent systems via decentralized output feedback stabilization approach

This article investigates the double dynamic event-triggered consensus of linear multiagent systems with periodic sampled-data via a novel decentralized output feedback stabilization approach. A novel dynamic event-triggered strategy based on periodic sampled-data is proposed for the sensor-to-controller channel and controller-to-actuator channel, respectively. This strategy can further reduce the number of triggers without affecting the system’s performance. We use a state linear transformation based on a directed spanning tree of the communication topology to equivalently transform the consensus problem into the decentralized output feedback stabilization problem of the corresponding edge-state system and propose a decentralized pole assignment approach to design the gain matrix for the consensus protocol. Then, by employing the Lyapunov function combined with the lossless S-procedure, we derive consensus criteria containing matrix inequalities. Finally, numerical examples are provided to verify the effectiveness of the proposed approach.

Water Molecules Adsorption, Stability, and Optoelectronic Characteristics of Pb‐Free Hybrid Double Perovskites Cs2AgInX6 (X = Br, Cl) for Solar Cells Application: A DFT Analysis

AbstractThe development of halide double perovskites has received a lot of interest from many researchers due to solving the problem of poor stability and toxicity of lead‐based perovskites, which hinders the commercialization of perovskite solar cells. Therefore, in this work, the adsorption of water molecules, stability, optical, and electronic properties of double perovskites Cs2AgInX6 (X = Br, Cl) are investigated using Density Functional Theory (DFT) calculations. Theoretical analysis shows that these double perovskites are thermodynamically stable. The diffusion coefficient of water in layers of Cs2AgInBr6 and Cs2AgInCl6 is much lower than that of MAPbI3 according to means square displacement analysis, and also based on values of adsorption energy, the hydrophilicity of the proposed structure is lower than that of PbI2‐terminated and MAI‐terminated surfaces. These materials demonstrate better ductility and mechanical stability than their corresponding 3D perovskites. For Cs2AgInBr6 and Cs2AgInCl6, direct bandgap values are 1.49 and 3.14 eV, respectively, using hybrid Perdew‐Berke‐Ernzerhof + spin‐orbit‐coupling(PBE0+SOC) functional. Calculations of key solar cell parameters predict that Cs2AgInBr6 may achieve efficiencies competitive with MAPbI3 due to its high short‐circuit current, making it a promising stable, non‐toxic perovskite absorber material. This work provides fundamental insights that can guide further research on double perovskites for lead‐free, moisture‐resistant perovskite solar technologies.

Environmental management of hotel: current issues of implementation

The problems of environmental stability and nature protection in the modern world are becoming increasingly important. In this aspect, an important tool is environmental management, or known as "eco-management", which plays the role of the most important factor in achieving sustainable development of enterprises, the desire to minimize negative consequences for nature. The article analyzes the use of eco-management in the hotel industry.

Uniform exponential stabilization for distributed discrete bilinear systems with time delay

In this paper we investigate the feedback stabilization problem for distributed discrete bilinear systems with time delay. Sufficient and necessary conditions for uniform exponential stabilization are given. Furthermore, under weaker conditions, the weak stabilization is achieved for the considered systems. Applications and illustrative simulations are presented.

Stability Analysis of Gravity‐Modulated Thermohaline Convection in Viscoelastic Fluid Saturating Porous Medium

ABSTRACTThis paper investigates the modified stability analysis of thermohaline convection in a horizontal Oldroyd‐B fluid using the Darcy model, with applications in geophysics, environmental engineering, material science, and biological systems. The basic equations of motion and heat conduction in the present model are based on the Darcy model and the modified Boussinesq approximation. The perturbation equations are derived using the power series perturbation method to study two‐dimensional convective roll instability with finite amplitude disturbances. Linear stability analysis, as a first‐order stability problem, provides expressions for the Rayleigh numbers for stationary and oscillatory convection. The influence of various parameters, including the Darcy–Prandtl number, solutal Rayleigh number, stress and strain retardation parameters, and variations in the coefficient of specific heat, on the stability of the considered system, is studied numerically. It is observed that an approximate 67% increase in the coefficient of specific heat variations and a 23% increase in the solutal Rayleigh number result on average increases of 80% and 8%, respectively, in the value of the oscillatory Darcy–Rayleigh number. Conversely, an average 42% increase in the Darcy–Prandtl number leads to an average decrease of 8% in the oscillatory Darcy–Rayleigh number. In the weakly nonlinear oscillatory analysis, second‐ and third‐order stability problems are discussed, and the Landau equation is derived, which describes the amplitudes of the convection cells. The effects of the parameters on heat and mass transfer rates, as described by the Nusselt and Sherwood numbers, are studied numerically. Furthermore, the weakly nonlinear stability analysis evaluates the effects of the Darcy–Prandtl number, specific heat coefficient, stress relaxation time, salinity Rayleigh number, strain retardation time, diffusivity ratio, and gravity modulation characteristics on heat and mass transfer rates. The effects of amplitude and frequency of gravity modulation on heat and mass transport are analyzed and depicted graphically. The study establishes that heat and mass transport can be effectively controlled by a mechanism external to the system. The results are validated by comparison with previous work, which considered a special case without the velocity gradient term in the momentum equation.

Identifying Land Use/Land Cover Changes Using Remote Sensing and GIS Techniques in Upper, Middle and Lower Reaches of Zayandeh-Rud Basin in Central Iran

The Zayandeh-Rud River basin, located in central Iran, has been one of the areas suffering from water instability problems. The water resource of the basin has diminished in the last decade, and consequently, the middle and downstream reaches of the river have temporarily dried or stopped flowing. Furthermore, there has been a serious decrease in water allocation to agricultural sector in these areas. In this study, ground-level land use changes were analyzed through Landsat satellite imagery analysis at two time periods, i.e., 2000 and 2014, which coincided with a period of instability in water resources of the Zayandeh-Rud River basin. The study area was divided into the upper, middle, and downstream reaches, and the results depicting areas under six land uses during 2000 and 2014 were compared to find changes in the land use. The results indicated that during these two periods of water resource instability, built-up and residential land uses all along the basin increased by 66.00 km2 ; therefore, the pasture land area decreased by 80.0 km2. Agricultural coverage in the upper reach increased by 108.85 km2; however, it decreased by 328.00 km2 in the middle reach and by 147.00 km2 in the lower reach. Conversely, barren land without cover decreased by 86 km2 in the upper reach, by 320.00 km2 in the middle reach, and by 183.00 km2 in the lower reach. According to the results of this study, some of the instability of agricultural water resources in the basin may have been intensified by the expansion of residential settlements, increase in agricultural land in the upper reach of the basin and generally mismanagement of land and water resources in the basin.

Modeling the motion of a ship with suspended cargo

The stability of a vessel determines its ability to safely navigate in any sea state. In the process of studying the dynamics of a vessel in rough seas, the method of mathematical modeling based on the linear theory of waves and rolling has been used. The models allow obtaining calculation formulas and methods used to analyze the rolling of vessels with shifting cargo on board (liquid, bulk, suspended). The effect of suspended cargo on the seaworthiness of a vessel is currently considered only when solving problems of static stability. When solving problems of dynamics, mathematical models of the roll of a vessel with suspended cargo in calm water and regular waves have been proposed, and linear differential equations of the roll of a vessel with suspended cargo have been obtained. The presence of suspended cargo on a vessel significantly changes the parameters of the roll due to the occurrence of heeling and variable moments of inertia of the vessel. The proposed mathematical methods allow simulating the roll in any regular waves, taking into account arbitrary values of the transverse metacentric height, cargo weight and suspension length.

The Riesz basisness of the eigenfunctions and eigenvectors connected to the stability problem of a fluid‐conveying tube with boundary control

AbstractIn the present paper we study the stability problem for a stretched tube conveying fluid with boundary control. The abstract spectral problem concerns operator pencils of the forms taking values in different Hilbert product spaces. Thorough analysis is made of the existence, location, multiplicities, and asymptotics of eigenvalues in the complex plane and Riesz basisness of the corresponding eigenfunctions and eigenvectors. Well‐posedness of the closed‐loop system represented by the initial‐value problem for the abstract equation is established in the framework of ‐semigroups as well as expansions of the solutions in terms of eigenvectors and stability of the closed‐loop system. For the parameters of the problem we give new regions, larger than those in the literature, in which a stretched tube with flow, simply supported at one end, with a boundary controller applied at the other end, can be exponentially stabilised.