Yantao Wang

Delay-dependent robust H ∞ filtering of uncertain stochastic genetic regulatory networks with mixed time-varying delays

In this paper, the robust H ∞ filtering problem for uncertain stochastic genetic regulatory networks (GRNs) with mixed time-varying delays is involved. The uncertain stochastic GRNs under consideration are extended to involve Ito-type stochastic disturbance, norm-bounded parameter uncertainties, and time-varying discrete and distributed delays. By constructing a proper Lyapunov-Krasovskii functional and using reciprocal convex technique, sufficient conditions in terms of linear matrix inequalities were presented to guarantee that the filtering error systems are mean-square robustly asymptotically stable with disturbance attenuation level γ. In the end, two numerical examples are given to illustrate the effectiveness of the proposed approach.

Finite-time stability for singular linear time-delay systems with time-varying exogenous disturbance

In this paper finite-time stability guaranteeing singular linear time-delay systems with time-varying exogenous disturbances is defined. A sufficient condition of the finite-time stability for this kind of systems is presented. Furthermore, the condition is reduced to feasible problems involving linear matrix inequalities. The effectiveness of the approach proposed in this paper is presented by a numerical example.

Fault-tolerant H ∞ control for descriptor linear systems via dynamical compensators

Fault-tolerant H∞ control against actuator failures and/or sensor failures for a class of descriptor linear systems via dynamical compensators is investigated. Based on H∞ theory in descriptor linear systems, sufficient conditions for the existence of dynamical compensators with parameters are derived. The dynamical compensator guarantees that the resulting closed-loop descriptor system is admissible and maintains a certain H∞ norm performance in the normal condition as well as in the event of actuator failures or/and sensor failures. Moreover, the closed-loop system performance can be optimized by choosing free parameters in designed dynamical compensators. A numerical example shows the effectiveness of the proposed method.

A reduced-order approach to analyze stability of genetic regulatory networks with discrete time delays

Abstract This paper addresses the problem of establishing the asymptotic stability criteria for genetic regulatory networks with discrete time delays. First, the system model is simplified to a reduced-order system with bounded uncertain parameters and distributed delays by exploiting calculus’s properties and Lagrange’s mean–value theorem. Second, the relationship between the asymptotic stability of the primal system and the robust asymptotic stability of the reduced-order one is investigated. Third, a new reduced-order approach is proposed to derive a sufficient condition for the robust asymptotic stability of the reduced-order system (i.e., the asymptotic stability of the primal system). At last, a numerical example illustrates the effectiveness of the theoretical results obtained in this paper.

Exponential passive filtering for a class of neutral-type neural networks with time-varying mixed delays

This paper is concerned with the problem of the exponential passive filter design for neutral-type neural networks with time-varying mixed delays. First, a Luenberger-type filter is designed for estimating the network states. Second, by constructing an appropriate Lyapunov-Krasovskii functional and using the so-called Wirtinger-based integral inequality to estimate its derivative, a delay-range-dependent and delay-rate-dependent criterion is presented to ensure the filtering error dynamic system to be exponentially stable and passive with an expected dissipation. Third, since the criterion is presented in the form of linear matrix inequalities with nonlinear constraints, a cone complementarity linearization algorithm is proposed to solve the nonlinear problem. Finally, a numerical example are given to demonstrate the effectiveness of the proposed method.

New delay-probability-distribution-dependent robust stability analysis for uncertain stochastic genetic regulatory networks with time-varying delays

This paper concerns the new delay-probability-distribution-dependent robust stability analysis for uncertain stochastic genetic regulatory networks (SGRNs) with time-varying delays. Based on model transformation, furthermore, by constructing a proper Lyaponov-Krasovskii functional and employing upper bound lemma on the reciprocally convex combination, we achieved the delay-probability-distribution-dependent criteria for the mean-square asymptotic stability of a class of SGRNs in terms of linear matrix inequalities (LMIs). The advantages of the proposed results compared some existing ones are to reduce computation complexity and conservativeness. Numerical examples show the effectiveness of the proposed approach.

Three stability criteria for delayed stochastic genetic regulatory networks and their conservativeness analysis

This paper considers the problem of stability analysis of a class of delayed genetic regulatory networks (GRNs) with stochastic disturbances. By introducing appropriate Lyapunov-Krasovskii functional and employing free-weighting matrix approach, convex combination approach and delay-range partition approach, respectively, three stability criteria in the form of linear matrix inequalities are established to guarantee the considered GRNs to be asymptotically stable in the mean square sense. The change rate of time-varying delays is assumed to be less than infinity. So, these stability criteria are applicable to both fast and slow change rate of time-varying delays. Then, theoretical and numerical comparisons are given to evaluate the conservativeness of the proposed stability criteria.

Robust fault-tolerant H ∞ control for uncertain descriptor systems by dynamical compensators

Robust fault-tolerant H∞ control against actuator failures and/or sensor failures is investigated for a class of uncertain descriptor systems via dynamical compensators. Based on H∞ theory, sufficient conditions for the existence of dynamical compensators are derived. The dynamical compensators guarantee that the closed-loop descriptor systems are admissible and maintain certain H∞ norm performance in the event of actuator failures and/or sensor failures as well as in the normal case. A simulation result shows the effectiveness of the proposed method.