The Analysis of Global Input-to-state Stability for Piecewise Affine Systems with Time-delay

In this paper, global input-to-state stability （ISS） for discrete-time piecewise affine systems with time-delay are considered Piecewise quadratic ISS-Lyapunov functions are adopted. Both Lyapunov-Razumikhiu and Lyapunov-Krasovskii methods are used The theorems of Lyapunov-Razumikhin type and Lyapunov-Krasovskii type for piecewise affine systems with time-delay are shown respectively.

Input-to-State Stabilization of Nonlinear Impulsive Delayed Systems: An Observer-Based Control Approach

This paper addresses the problems of input-to-state stabilization and integral input-to-state stabilization for a class of nonlinear impulsive delayed systems subject to exogenous dis-turbances.Since the information of plant’s states,time delays,and exogenous disturbances is often hard to be obtained,the key design challenge,which we resolve,is the construction of a state observer-based controller.For this purpose,we firstly propose a corresponding observer which is independent of time delays and exogenous disturbances to reconstruct(or estimate)the plant’s states.And then based on the observations,we establish an observer-based control design for the plant to achieve the input-to-state stability(ISS)and integral-ISS(iISS)properties.With the help of the comparison principle and average impulse interval approach,some sufficient conditions are presented,and moreover,two different linear matrix inequalities(LMIs)based criteria are proposed to design the gain matrices.Finally,two numerical examples and their simulations are given to show the effectiveness of our theoretical results.

Analysis of finite-time practical stability for time-varying polytopic systems

The problem of finite-time practical stability （FTPS） for time-varying polytopic systems is discussed. Three equivalent conditions for FTPS are first proposed. To facilitate the system analysis, a sufficient linear matrix inequality （LMI） criterion on the FTPS is further provided. The definition of finite-time practical boundedness and a sufficient LMI criterion are also provided to overcome the exogenous disturbance. A numerical example is used to illustrate the effect of the proposed approach.

NON-INSTANTANEOUS IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS WITH STATE DEPENDENT DELAY AND PRACTICAL STABILITY

Nonlinear delay Caputo fractional differential equations with non-instantaneous impulses are studied and we consider the general case of delay,depending on both the time and the state variable.The case when the lower limit of the Caputo fractional derivative is fixed at the initial time,and the case when the lower limit of the fractional derivative is changed at the end of each interval of action of the impulse are studied.Practical stability properties,based on the modified Razumikhin method are investigated.Several examples are given in this paper to illustrate the results.

Practical Stability Analysis of Linear Impulsive Hybrid Systems Involving Fractional Derivatives

Practical stabilities for linear fractional impulsive hybrid systems are investigated in detail.The transformation from a linear fractional differential system to a fractional impulsive hybrid system is interpreted.With the help of the Mittag-Leffler functions for matrix-type,several practical stability criteria for fractional impulsive hybrid systems are derived.Finally,a numerical example is provided to illustrate the effectiveness of the results.

Practical Stability Analysis and Synthesis of Linear Descriptor Systems with Disturbances

This paper considers the problems of practical stability analysis and synthesis of linear descriptor systems subject to timevarying and norm-bounded exogenous disturbances. A sufficient condition for the systems to be regular, impulsive-free and practically stable is derived. Then the synthesis problem is addressed and a state feedback controller is designed. To deal with the computational issue, the conditions of the main results are converted into linear matrix inequality （LMI） feasibility problems. Furthermore, two optimization algorithms are formulated to improve the system performances. Finally, numerical examples are given to illustrate the obtained results.

Practical stability and instability of regime-switching diffusions

This work is devoted to practical stability of a class of regime-switching diffusions. First, the notion of practical stability is introduced. Then, sufficient conditions for practical stability and practical instability in probability and in pth mean are provided using a Lyapunov function argument. In addition, easily verifiable conditions on drift and diffusion coefficients are also given. Moreover, examples are supplied for demonstration purposes.

On the conjunction practical stability and controllability of large-scale impulsive control systems

We studied the conjunction practical stability and controllability of large-scale impulsive control systems by using the comparison systems and vector Lyapunov fimctions. Then the less conservative sufficient conditions for conjunction practical stability and controllability of large-scale impulsive control system were obtained.

Practical Stability in the pth Mean of Stochastic Differential Equations with Discontinuous Coefficients

In this paper,we give sufficient conditions to analyze the practical stability in the pth mean of stochastic differential equations with discontinuous coefficients.The Lyapunov-like function plays an important role in analysis.Some numerical computations are carried out to illustrate the theoretical results.

How Does Heat-Stress Intensity Affect the Stability of Microbial Activity and Diversity of Soil Microbial Communities in Outfields and Homefields’ Cultivation Practices in the Senegalese Groundnut Basin?

Agroecosystems in the Senegalese groundnut basin experience long periods of high temperatures and drought, which disrupt the stability of soil microbial communities. This study evaluated how that stability is affected by homefields and outfields’ agricultural practices and the duration of heat stress. Specifically, we collected soils from organically farmed fields that receive continual high inputs of manure (homefields), and from fields that are rarely manured (outfields). Soil samples were submitted to artificial heat stress at 60°C for 3, 14, and 28 days, followed by 28 days of recovery at 28°C. We examined the functional stability of microbial communities by quantifying C mineralization, and characterized the stability of the communities’ taxonomic compositions via high-throughput DNA sequencing. We found that the microbial communities have a low resistance to heat stress in soils from both types of fields. However, the manuring practice does affect how the functional stability of microbial communities responds to different durations of heat stress. Although functional stability was not recovered fully in either soil, microbial community resilience seemed to be greater in homefield soils. Differences in manuring practices also affected the structural taxonomic stability of microbial communities: relative abundances of Bacilli, Chloroflexia, Actinobacteria and Sordariomycetes increased in the homefield stressed-soils, but decreased significantly in outfield soils. In contrast, relative abundances of α-Proteobacteria, γ-Proteobacteria and Eurotiomycetes increased significantly in outfield stressed-soils, while decreasing significantly in the homefield soils. Relative abundances of Bacilli changed little in outfield soils, indicating that this taxon is resistant to heat stress. In summary, the microbial communities’ capacities to resist heat stress and recover from it depend upon the organic richness of the soil (i.e., manuring practice) and the adaptation of soil microbes to environmental conditions.

Practical φ_0-stability of stochastic differential equations and corresponding stochastic perturbation theory

The notions of practical φ0-stability were introduced for stochastic differential equations. Sufficient conditions on such practical properties were obtained by using the comparison principle and the cone-valued Lyapunov function methods. Based on an extended comparison theorem, a perturbation theory of stochastic differential systems was given.

Global Practical Stabilization of Discrete-Time Switched Affine Systems via a General Quadratic Lyapunov Function and a Decentralized Ellipsoid

This paper addresses the problem of global practical stabilization of discrete-time switched affine systems via statedependent switching rules.Several attempts have been made to solve this problem via different types of a common quadratic Lyapunov function and an ellipsoid.These classical results require either the quadratic Lyapunov function or the employed ellipsoid to be of the centralized type.In some cases,the ellipsoids are defined dependently as the level sets of a decentralized Lyapunov function.In this paper,we extend the existing results by the simultaneous use of a general decentralized Lyapunov function and a decentralized ellipsoid parameterized independently.The proposed conditions provide less conservative results than existing works in the sense of the ultimate invariant set of attraction size.Two different approaches are proposed to extract the ultimate invariant set of attraction with a minimum size,i.e.,a purely numerical method and a numerical-analytical one.In the former,both invariant and attractiveness conditions are imposed to extract the final set of matrix inequalities.The latter is established on a principle that the attractiveness of a set implies its invariance.Thus,the stability conditions are derived based on only the attractiveness property as a set of matrix inequalities with a smaller dimension.Illustrative examples are presented to prove the satisfactory operation of the proposed stabilization methods.

Practical stabilization of receding-horizon control

The purpose of this work is to propose a scheme to stabilize the predictive control systems in the practical stability sense. In the paper, the authors dealt with a general discrete predictive control system x j+1|t =f(x j|t , u j|t ) by using the Lyapunov direct method combining with receding horizon control technique, and presented a new condition to guarantee the practical stabilization of the systems. With the proposed results, one can design the optimal controllers easily to practically stabilize the predictive control systems.

Practical Stabilization of Counterfactual Quantum Cryptography

A novel counterfactual quantum key distribution scheme was proposed by T.-G. Noh and a strict security analysis has been given by Z.-Q.Yin, in which two legitimate geographical separated couples may share secret keys even when the key carriers are not traveled in the quantum channel. However, there are still plenty of practical details in this protocol that haven’t been discussed yet, which are of significant importance in physical implementation. In this paper, we will give a practical analysis on such kind of counterfactual quantum cryptography in the aspects of quantum bit error rate (QBER) and stabilization. Furthermore, modified schemes are proposed, which can obtain lower QBER and will be much more robust on stabilization in physical implementation.

Practical Stabilization for Uncertain Pseudo-Linear and Pseudo-Quadratic MIMO Systems

In this paper the problem of practical stabilization for a significant class of MIMO uncertain pseudo-linear and pseudo-quadratic systems, with additional bounded nonlinearities and/or bounded disturbances, is considered. By using the concept of majorant system, via Lyapunov approach, new fundamental theorems, from which derive explicit formulas to design state feedback control laws, with a possible imperfect compensation of nonlinearities and disturbances, are stated. These results guarantee a specified convergence velocity of the linearized system of the majorant system and a desired steady-state output for generic uncertainties and/or generic bounded nonlinearities and/or bounded disturbances.

Input-to-State Stability for Impulsive Switched Singular Systems with Mismatched Disturbances

This work investigates the input-to-state stability(ISS)problem for impulsive switched singular systems(ISSSs)with mismatched disturbances.In this paper,‘disturbance’is a general concept that includes model uncertainty,unknown system dynamic,external disturbance,etc.The modified uncertainty and disturbance estimator(UDE)-based control method is presented for singular systems and ISSSs,a virtual control is introduced to offset the effects of mismatched disturbances.On the basis of a discontinuous multiple Lyapunov functional and admissible edge-dependent average dwell time(AED-ADT)method,several sufficient conditions in terms of linear matrix inequalities(LMIs)are obtained to ensure that the closed-loop systems are regular,impulse-free and ISS.Finally,two examples are given to demonstrate the effectiveness of the proposed results.

Estimation of LISS(local input-to-state stability) properties for nonlinear systems

Compared with input-to-state stability(ISS) in global version,the concept of local input-to-state stability(LISS) is more relevant and meaningful in practice.The key of assessing LISS properties lies in investigating three main ingredients,the local region of initial states,the local region of external inputs and the asymptotic gain.It is the objective of this paper to propose a numerical algorithm for estimating LISS properties on the theoretical foundation of quadratic form LISS-Lyapunov function.Given developments of linear matrix inequality(LMI) methods,this algorithm is effective and powerful.A typical power electronics based system with common DC bus is served as a demonstration for quantitative results.

A Notion of Stochastic Input-to-State Stability and Its Application to Stability of Cascaded Stochastic Nonlinear Systems

In this paper, the property of practical input-to-state stability and its application to stability of cascaded nonlinear systems are investigated in the stochastic framework. Firstly, the notion of （practical） stochastic input-to-state stability with respect to a stochastic input is introduced, and then by the method of changing supply functions, （a） an （practical） SISS-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for cascaded （practical） SISS subsystems.

Input-to-State Stability of Switched Nonlinear Delay Systems Based on a Novel Lyapunov-Krasovskii Functional Method

In this paper, the input-to-state stability （ISS） analysis is addressed for switched nonlinear delay systems. By introducing a novel Lyapunov-Krasovskii functional with indefinite derivative and the merging switching signal techniques, some new- criteria are established for switched nonlinear delay systems under asynchronous switching, which extends the existing results to the nonlinear systems with switching rules and delays. The ISS problem is also considered under synchronous switching for switched nonlinear systems by employing the similar techniques. Finally, a nonlinear delay model is provided to show the effectiveness of the proposed results.

Input-to-state stability of switched nonlinear systems

The input-to-state stability （ISS） problem is studied for switched systems with infinite subsystems. By using multiple Lyapunov function method, a sufficient ISS condition is given based on a quantitative relation of the control and the values of the Lyapunov functions of the subsystems before and after the switching instants. In terms of the average dwell-time of the switching laws, some sufficient ISS conditions are obtained for switched nonlinear systems and switched linear systems, respectively.