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.

Global practical stabilization of the double integrator system with an imperfect sensor and subject to a bounded disturbance

This paper is concerned with global practical stabilization of the double integrator system with an imperfect sensor and subject to an additive bounded output disturbance.The imperfect sensor nonlinearity possesses the nonlinear characteristics of saturation and dead zone.Because of the presence of output dead zone and the additive disturbance,the states cannot be expected to driven into an arbitrarily small neighborhood of the origin.To solve the global practical stabilization problem,we proposes a low gain-based linear dynamic output feedback law,under which the first state enters and remains in a bounded set whose size is depended on the bound of disturbance and the range of dead zone and the second state enters and remains in a pre-specified arbitrarily small set,both in finite time.Simulation results illustrate the effectiveness of our proposed control method.

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.

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.

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.

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 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.

On the model-based networked control for singularly perturbed systems

In this paper, the control of a two-time-scale plant, where the sensor is connected to a linear controller/ actuator via a network is addressed. The slow and fast systems of singularly perturbed systems are used to produce an estimate of the plant state behavior between transmission times, by which one can reduce the usage of the network. The approximate solutions of the whole systems are derived and it is shown that the whole systems via the network control are generally asymptotically stable as long as their slow and fast systems are both stable. These results are also extended to the case of network delay.

Engineering rock mechanics practices in the underground powerhouse at JinpingⅠhydropower station

Based on the analyses of data obtained from the underground powerhouse at Jinping I hydropower station, a comprehensive review of engineering rock mechanics practice in the underground powerhouse is first conducted. The distribution of strata, lithology, and initial geo-stress, the excavation process and corresponding rock mass support measures, the deformation and failure characteristics of the surrounding rock mass, the stress characteristics of anchorage structures in the cavern complex, and numerical simulations of surrounding rock mass stability and anchor support performance are presented. The results indicate that the underground powerhouse of Jinping I hydropower station is characterized by high to extremely high geo-stresses during rock excavation. Excessive surrounding rock mass deformation and high stress of anchorage structures, surrounding rock mass unloading damage, and local cracking failure of surrounding rock masses, etc., are mainly caused by rock mass excavation. Deformations of surrounding rock masses and stresses in anchorage structures here are larger than those found elsewhere： 20% of extensometers in the main powerhouse record more than 50 mm with the maximum at around 250 mm observed in the downstream sidewall of the transformer hall. There are about 25% of the anchor bolts having recorded stresses of more than 200 MPa. Jinping I hydropower plant is the first to have an underground powerhouse construction conducted in host rocks under extremely high geo-stress conditions, with the ratio of rock mass strength to geo-stress of less than 2.0. The results can provide a reference to underground powerhouse construction in similar geological conditions.

Semi-Global Practical Stability of Random Systems and Its Application

In this paper,a new stochastic analysis tool on semi-global stability is constructed,for nonlinear systems disturbed by stochastic processes with strongly bounded in probability.The definition of semi-global noise to state practical stability in probability and its Lyapunov criterion for random systems are presented.As a major application of stability,the semi-global practical tracking of random nonlinear systems based on dynamic surface control technique is considered.The trajectory tracking of manipulator robot driven by direct current motors is carried out in simulation to illustrate the effectiveness and feasibility of the control scheme.

Practical Exponential Stability of Two Dimensional Nonlinear Switched Positive Systems in the Roesser Model

This paper deals with the practical exponential stability of two-dimensional(2-D)nonlinear switched positive systems with impulse,disturbance and all modes unstable.Under the mode-dependent interval dwell time switching,new criteria such that 2-D nonlinear switched positive systems achieve practical exponential stability are derived.Furthermore,the explicit upper bound and convergence rate of the system state are estimated explicitly.Numerical examples indicate the correctness and effectiveness of the obtained results.

PRACTICAL STABILITY OF DYNAMIC SYSTEMS WITH IMPULISIVE SOLUTIONS

Practical stability problems of single dynamic system with impulsive solutions are considered in this paper. Using comparison principle, a class of Vk functions and impulsive differential inequalities, the criteria of practical stability, practical uniform stability and practical instability of such kind of system are obtained and proved. The results which are obtained here have improved on the results in reference [5]

PRACTICAL STABILITY IN TERMS OF TWO MEASURES FOR DISCRETE SYSTEMS

Practical stability in terms of two measures for difference equations is discussed by using the Lyapunov function and a new comparison theorem.