Feiqi Deng

Noise suppresses or expresses exponential growth

In this paper we will show that noise can make a given system whose solutions grow exponentially become a new system whose solutions will grow at most polynomially. On the other hand, we will also show that noise can make a given system whose solutions are bounded become a new system whose solutions will grow exponentially. In other words, we reveal that the noise can suppress or expresses exponential growth.

Stochastic stabilization of hybrid differential equations

This paper aims to determine whether or not a stochastic state feedback control can stabilize a given linear or nonlinear hybrid system. New methods are developed and sufficient conditions on the stability for hybrid stochastic differential equations are provided. These results are then used to examine stochastic stabilization by stochastic feedback controls. Two types of structure controls, namely state feedback and output injection, are discussed. Our stabilization criteria are in terms of linear matrix inequalities (LMIs) whence the feedback controls can be designed more easily in practice. A couple of examples and computer simulations are worked out to illustrate our theory.

Stability of Hybrid Stochastic Retarded Systems

In the past few years, hybrid stochastic retarded systems (also known as stochastic retarded systems with Markovian switching), including hybrid stochastic delay systems, have been intensively studied. Among the key results, Mao et al. proposed the Razumikhin-type theorem on exponential stability of stochastic functional differential equations with Markovian switching and its application to hybrid stochastic delay interval systems. However, the importance of general asymptotic stability has not been considered. This paper is to study Razumikhin-type theorems on general p-th moment asymptotic stability of hybrid stochastic retarded systems. The proposed theorems apply to complex systems including some cases when the existing results cannot be used.

Exponential stability analysis of impulsive stochastic functional differential systems with delayed impulses

Abstract This paper is concerned with the exponential stability analysis of impulsive stochastic functional differential systems with delayed impulses. Although the stability of impulsive stochastic functional differential systems have received considerable attention. However, relatively few works are concerned with the stability of systems with delayed impulses and our aim here is mainly to close the gap. Based on the Lyapunov functions and Razumikhin techniques, some exponential stability criteria are derived, which show that the system will stable if the impulses’ frequency and amplitude are suitably related to the increase or decrease of the continuous flows. The obtained results improve and complement ones from some recent works. Three examples are discussed to illustrate the effectiveness and the advantages of the results obtained.

Palm vein recognition based on multi-sampling and feature-level fusion

Abstract For contactless palm vein images, particularly substantial changes in hand positioning between one image and the next, it is difficult to achieve a satisfactory recognition performance with geometry- or statistics-based methods due to issues such as non-uniform illumination and affine transformation. Therefore, with a multi-sampling and feature-level fusion strategy, a novel palm vein recognition method based on local invariant features is presented for addressing the aforementioned issues. As most of the contactless palm vein images are unclear and have low contrast, if a SIFT algorithm is directly adopted for feature extraction on the center region of a palm vein image, it will be difficult to obtain sufficient features for effective recognition. Therefore, in this paper, we first propose to take the entire palm as a Region of Interest (ROI) and perform new hierarchical enhancement on the ROI to ensure that additional features will be obtained from the subsequent feature extraction. Then, we take full advantage of the multiple samples collected in the registration stage to generate the registered template using feature-level fusion. Finally, bidirectional matching is proposed for mismatch removal. The experiments on the CASIA Palm vein Image Database and our palm vein database collected under the posture changes show that the proposed method was superior in terms of recognition performance, especially for palm vein image recognition under remarkable posture changes. In particular, the values of Equal Error Rate (EER) on the aforementioned two databases were 0.16% and 0.73%, respectively.

Moment stability of nonlinear discrete stochastic systems with time-delays based on H-representation technique

In this paper, mean square stability of nonlinear discrete stochastic systems with time-delays is investigated. We obtain the second order moment equations of discrete stochastic systems by virtue of the H-representation technique. By the comparison principle and the established moment equations, some moment stability theorems for nonlinear discrete stochastic systems with time-delays are established. A numerical example is presented to illustrate the efficiency of our results at the end of the paper.

Robust H 2/H ∞ global linearization filter design for nonlinear stochastic time-varying delay systems

One can design a robust H∞ filter for a general nonlinear stochastic system with external disturbance by solving a second-order nonlinear stochastic partial Hamilton-Jacobi inequality (HJI), which is difficult to be solved. In this paper, the robust mixed H2/H∞ globally linearized filter design problem is investigated for a general nonlinear stochastic time-varying delay system with external disturbance, where the state is governed by a stochastic Itô-type equation. Based on a globally linearized model, a stochastic bounded real lemma is established by the Lyapunov–Krasovskii functional theory, and the robust H∞ globally linearized filter is designed by solving the simultaneous linear matrix inequalities instead of solving an HJI. For a given attenuation level, the H2 globally linearized filtering problem with the worst case disturbance in the H∞ filter case is known as the mixed H2/H∞ globally linearized filtering problem, which can be formulated as a linear programming problem with simultaneous LMI constraints. Therefore, this method is applicable for state estimation in nonlinear stochastic time-varying delay systems with unknown exogenous disturbance when state variables are unavailable. A simulation example is provided to illustrate the effectiveness of the proposed method.

Decentralized state feedback adaptive tracking for a class of stochastic nonlinear large-scale systems

In this paper, decentralized adaptive tracking problem is studied for a class of stochastic nonlinear large-scale systems, which can be parameterized. The systems are transformed into parameterized strict-feedback nonlinear large-scale form through coordinate transformation at first. By employing the stochastic Lyapunov-like theorem and the backstepping design technique, the adaptive state feedback decentralized controller and parameters adaptive law are developed. The output of the closed-loop system is proven to follow the desired trajectory asymptotically in probability.

Stability of impulsive stochastic functional differential systems in terms of two measures via comparison approach

Comparison principles for general impulsive stochastic functional differential systems are established. Employing the comparison principles and the theory of differential inequalities, stability and instability, involving two measures, of impulsive stochastic functional differential systems are investigated. Several stability and instability criteria are obtained, and two examples are also given to illustrate our results.

Exponential Stability of Impulsive Stochastic Functional Differential Systems with Delayed Impulses

A class of generalized impulsive stochastic functional differential systems with delayed impulses is considered. By employing piecewise continuous Lyapunov functions and the Razumikhin techniques, several criteria on the exponential stability and uniform stability in terms of two measures for the mentioned systems are obtained, which show that unstable stochastic functional differential systems may be stabilized by appropriate delayed impulses. Based on the stability results, delayed impulsive controllers which mean square exponentially stabilize linear stochastic delay systems are proposed. Finally, numerical examples are given to verify the effectiveness and advantages of our results.