Guang-Da Hu

Converse Lyapunov Theorem of Input-to-State Stability for Time-delay Systems

Abstract This paper is concerned with locally Lipschitz continuous converse Lyapunov theorem of input-to-state stability for time-delay systems. For time-delay systems with arbitrary measurable locally essentially bounded disturbances, it is shown that a locally Lipschitz continuous Lyapunov functional exists if these systems are robustly asymptotically stable. Under this result, the Lyapunov characterizations of input-to-state stability for time-delay systems are obtained.

Consensus of Linear Multi-Agent Systems with Communication and Input Delays

Abstract In this paper, we consider the consensus problem of a group of general linear agents with communication and input delays under a fixed, undirected network topology. By factorizing the characteristic equation of the multi-agent system into a set of reduced-order factors, the problem is transformed to the stability analysis of resulting factors with reduction in complexity. Furthermore, stable ranges of the control gain, such that the consensus of multi-agent systems could be reached when delays vanish, are analyzed. With control gain confined to stable ranges, and applying the advanced clustering with frequency sweeping method to investigate the stability of factors, the delay-independent and delay-dependent consensus are discussed. An illustrative example is offered to verify the analytical conclusions.

Stability Analysis for Uncertain Nonlinear Time-delay Systems with Quasi-one-sided Lipschitz Condition

Abstract This paper deals with the robust stability of a class of uncertain nonlinear time-delay systems. A quasi-one-sided Lipschitz condition is introduced to estimate the influence of nonlinear vector function on the stability analysis. Delay-independent/delay-dependent stability criteria formulated in the form of linear matrix inequalities are presented. Furthermore, these stability criteria are available even if the system parameter is unstable, because the unnecessary positive quasi-one-sided Lipschitz constant matrix includes much useful information of the nonlinear part. Numerical examples show the advantage of the results obtained in this paper.

State Estimation of 2-D Stochastic Systems Represented by FM-II Model

Abstract This paper is concerned with state estimation of two-dimensional (2-D) discrete stochastic systems. First, 2-D discrete stochastic system model is established by extending system matrices of the well-known Fornasini-Marchesini s second model into stochastic matrices. Each element of these stochastic matrices is second-order weakly stationary white noise sequences. Secondly, a linear and unbiased full-order state estimation problem for 2-D discrete linear stochastic model is formulated. Two estimation problems considered are the designs for the mean-square bounded estimation error and for the mean-square stochastic version of the suboptimal H ∞ estimator, respectively. Our results can be seen as extensions of the 2-D linear deterministic case. Finally, illustrative examples are provided.

Mean-square Exponential Input-to-state Stability of Euler-Maruyama Method Applied to Stochastic Control Systems

Abstract This paper deals with the mean-square exponential input-to-state stability (exp-ISS) of Euler-Maruyama (EM) method applied to stochastic control systems (SCSs). The aim is to find out the conditions of the exact and EM method solutions to an SCS having the property of mean-square exp-ISS without involving control Lyapunov functions. Second moment boundedness and an appropriate form of strong convergence are achieved under global Lipschitz coefficients and mean-square continuous random inputs. Under the strong convergent condition, it is shown that the mean-square exp-ISS of an SCS holds if and only if that of the EM method is preserved for sufficiently small step size.

Computation of Unstable Characteristic Roots of Neutral Delay Systems

Abstract We present an algorithm based on the argument principle for computing all unstable characteristic roots of a class of neutral time delay systems. By consecutively subdividing a bounded rectangular or half circular region on the right half complex plane into smaller ones, initial approximate positions of all unstable roots can be located efficiently. With these approximate positions as starting points for Newtons method, approximations for all roots are refined iteratively. The performance of the algorithm is shown by an example.

Mean-Square Exponential Input-to-State Stability of Numerical Solutions for Stochastic Control Systems

Abstract This paper deals with the mean-square exponential input-to-state stability (exp-ISS) of numerical solutions for stochastic control systems (SCSs). Firstly, it is shown that a finite-time strong convergence condition holds for the stochastic θ-method on SCSs. Then, we can see that the mean-square exp-ISS of an SCS holds if and only if that of the stochastic θ-method (for sufficiently small step sizes) is preserved under the finite-time strong convergence condition. Secondly, for a class of SCSs with a one-sided Lipschitz drift, it is proved that two implicit Euler methods (for any step sizes) can inherit the mean-square exp-ISS property of the SCSs. Finally, numerical examples confirm the correctness of the theorems presented in this study.

Discretization of Continuous-time Systems with Input Delays

Abstract In this paper, the Runge-Kutta (RK) method, which involves the polynomial interpolation is adopted to discretize continuous-time systems with input delay. The proposed scheme is an efficient and higher-order approach compared with conventional discretizing methods. The accuracy of the proposed conversion scheme is closely related to the order of RK as well as that of the polynomial interpolation. Both the approximate order and the maximal attainable order of the discretization are discussed. In addition, the input-to-state stability of the scheme is analyzed. In order to guarantee the stability of the corresponding discrete system, the sampling time can be chosen by investigating the absolute stability region of the RK method. Especially, when the RK method is A-stable, the sampling time can be selected without being constrained by stability considerations. A numerical experiment is provided to demonstrate the superior performance of the method.

Asymptotic Stability of 2-D Positive Linear Systems with Orthogonal Initial States

Abstract This paper deals with the asymptotic stability of 2-D positive linear systems with orthogonal initial states. Different from the 1-D systems, the asymptotic stability of 2-D systems with orthogonal initial states x(i, 0), x(0, j) (Fornasini-Marchesini (FM) model) or xv (i, 0), xh (0, j) (Roesser model) is strictly dependent on proper boundary conditions. Firstly, an asymptotic stability criterion for 2-D positive FM first model is presented by making initial states x(i, 0), x(0, j) absolutely convergent. Then, a similar result is also given for 2-D positive Roesser model with any absolutely convergent initial states xv (i, 0), xh (0, j). Finally, two examples are given to show the effectiveness of these criteria and to demonstrate the convergence of the trajectories by making exponentially convergent initial states.