Yuangong Sun

Average consensus in networks of dynamic agents with uncertain topologies and time-varying delays

Abstract In this paper, we study average consensus problem in networks of dynamic agents with uncertain topologies as well as time-varying communication delays. By using the linear matrix inequality method, we establish several sufficient conditions for average consensus in the existence of both uncertainties and delays. Several linear matrix inequality conditions are presented to determine the allowable upper bounds of time-varying communication delays and uncertainties. Numerical examples are worked out to illustrate the theoretical results.

Some nonlinear dynamic integral inequalities on time scales

In this paper, we study some dynamic integral inequalities with mixed nonlinearities on time scales, which provide explicit bounds on unknown functions. Our results include many existing ones in the literature as special cases and can be used as tools in the qualitative theory of certain classes of dynamic equations with mixed nonlinearities on time scales.

On the existence of linear copositive Lyapunov functions for 3-dimensional switched positive linear systems

Abstract This paper is focused on deriving easily verifiable conditions for the existence of common linear copositive Lyapunov functions for 3-dimensional switched positive linear systems. Unlike some results in the literature, the existence of a common linear copositive Lyapunov function is only determined by two constants given in terms of the entries of system matrices. The structure of all common linear copositive Lyapunov functions is characterized clearly. We also extend the main result to the discrete case and the case of control input.

Finite-time stability for impulsive switched delay systems with nonlinear disturbances

This paper investigates finite-time stability (FTS) for impulsive switched delay systems which allow the disturbances may have stronger nonlinearities. Based on novel inequalities technique and average dwell time approach, several stability criteria are established to guarantee that the state trajectory of the system does not exceed a certain threshold over a pre-specified finite time interval. Two examples are also provided to illustrate the effectiveness of the theoretical results.

State bounding for homogeneous positive systems of degree one with time-varying delay and exogenous input☆

Abstract This paper considers the problem of state bounding for homogeneous positive systems of degree one with time-varying delay and exogenous input. In both the continuous-time case and the discrete-time case, necessary and sufficient conditions are derived for the existence of a ball where all the solutions of the system converge exponentially within. Numerical examples are also given to illustrate the obtained results.

Asymptotic behavior of switched delay systems with nonlinear disturbances

The objective of this paper is to study the asymptotic behavior of switched delay systems with nonlinear disturbances. By establishing a new delay Gronwall-Bellman integral inequality and an elementary inequality, we obtain some asymptotic results for the systems under arbitrary switching laws, which extend some existing results in the literature to the more general nonlinear case. Finally, two examples are provided to illustrate the effectiveness of our results.

Exponential stabilization of switched time-varying systems with delays and disturbances

Abstract This paper deals with exponential stabilization for a class of switched time-varying systems. By taking time-varying delays and nonlinear disturbances into consideration, time dependent switching signals have been characterized in terms of Metzler matrices such that the resulting system is globally exponentially stable. Compared with preceding works, we introduce a model transformation and an approach without involving the Lyapunov-Krasovskii functional to derive new exponential stability criteria for switched time-varying systems under the average dwell time switching. Numerical examples show that the obtained theoretical results can be applied to some cases not covered by some existing results.

Comparison criteria for odd order forced nonlinear functional neutral dynamic equations

The purpose of this paper is to establish comparison criteria for forced odd order neutral dynamic equation x ( t ) + p ( t ) x ( ? ( t ) ) n + q t ? γ x ? t = g ( t ) , on an above-unbounded time scale T , where n ? 3 ; ? γ ( u ) ? u γ - 1 u , γ 0 ; p , q ? C rd t 0 , ∞ T , R + on t 0 , ∞ T ; g ? C rd ( t 0 , ∞ ) T , R ) ; and ? , ? : T ? T are rd-continuous functions such that lim t ? ∞ ? ( t ) = lim t ? ∞ ? ( t ) = ∞ . Comparison criteria have been established without assuming certain restrictive conditions on the time scale T which improve some results in a number of recent papers.

Common joint linear copositive Lyapunov functions for positive switched systems

Abstract Unlike many papers focusing on common linear copositive Lyapunov functions (CLCLFs) for positive switched systems, this paper studies the existence of a class of common weak linear copositive Lyapunov functions called common joint linear copositive Lyapunov functions (CJCLFs). Necessary and sufficient conditions for the existence of CJCLFs are established. The conditions are easily verifiable via the straightforward computation, and can be applied to the asymptotic stability problem of the positive switched linear system when each switching mode is only Lyapunov stable.

Common Weak Linear Copositive Lyapunov Functions for Positive Switched Linear Systems

Lyapunov functions play a key role in the stability analysis of complex systems. In this paper, we study the existence of a class of common weak linear copositive Lyapunov functions (CWCLFs) for positive switched linear systems (PSLSs) which generalize the conventional common linear copositive Lyapunov functions (CLCLFs) and can be used as handy tool to deal with the stability of PSLSs not covered by CLCLFs. We not only establish necessary and sufficient conditions for the existence of CWCLFs but also clearly describe the algebraic structure of all CWCLFs. Numerical examples are also given to demonstrate the effectiveness of the obtained results.