Wei Xing Zheng

Brief paper: Second-order consensus in multi-agent dynamical systems with sampled position data

This paper studies second-order consensus in multi-agent dynamical systems with sampled position data. A distributed linear consensus protocol with second-order dynamics is designed, where both the current and some sampled past position data are utilized. It is found that second-order consensus in such a multi-agent system cannot be reached without any sampled position data under the given protocol while it can be achieved by appropriately choosing the sampling period. A necessary and sufficient condition for reaching consensus of the system in this setting is established, based on which consensus regions are then characterized. It is shown that if all the eigenvalues of the Laplacian matrix are real, then second-order consensus in the multi-agent system can be reached for any sampling period except at some critical points depending on the spectrum of the Laplacian matrix. However, if there exists at least one eigenvalue of the Laplacian matrix with a nonzero imaginary part, second-order consensus cannot be reached for sufficiently small or sufficiently large sampling periods. In such cases, one nevertheless may be able to find some disconnected stable consensus regions determined by choosing appropriate sampling periods. Finally, simulation examples are given to verify and illustrate the theoretical analysis.

Dissipativity-Based Sliding Mode Control of Switched Stochastic Systems

This technical brief is concerned with dissipativity analysis and dissipativity-based sliding mode control (SMC) of continuous-time switched stochastic systems. Firstly, a sufficient condition is proposed to guarantee the mean-square exponential stability and strict dissipativity for the switched stochastic system. Then, an integral-type sliding surface function is designed for establishing a sliding mode dynamics, which can be formulated by a switched stochastic system with an external disturbance/uncertainty. Dissipativity analysis and synthesis are both investigated for the sliding mode dynamics, and consequently sufficient conditions are derived, which pave the way for solving the dissipativity analysis and control problems. Moreover, a SMC law is synthesized to drive the system trajectories onto the predefined sliding surface in a finite time. Finally, the efficiency of the theoretical findings is demonstrated by an illustrative example.

Brief paper: Passivity-based sliding mode control of uncertain singular time-delay systems

In this paper the problem of sliding mode control (SMC) with passivity of a class of uncertain nonlinear singular time-delay systems is studied. An integral-type switching surface function is designed by taking the singular matrix into account, thus the resulting sliding mode dynamics is a full-order uncertain singular time-delay system. By introducing some slack matrices, a delay-dependent sufficient condition is proposed in terms of linear matrix inequality (LMI), which guarantees the sliding mode dynamics to be generalized quadratically stable and robustly passive. The passification solvability condition is then established. Moreover, a SMC law and an adaptive SMC law are synthesized to drive the system trajectories onto the predefined switching surface in a finite time. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory.

Brief paper: Delay-dependent robust stabilization for uncertain neutral systems with distributed delays

The problems of robust stability and robust stabilization of uncertain neutral systems with distributed delays are studied in this paper. Using a combination of integral inequality technique and descriptor system approach, new delay-dependent sufficient conditions for robust stability and robust stabilization are formulated in terms of linear matrix inequalities (LMIs). LMI-based conditions are also derived for robust stability and robust stabilizability of uncertain distributed-delay systems when the distributed delay belongs to a given interval. When the results obtained in this paper are applied to stabilization of combustion in the chamber of a liquid monopropellant rocket motor, it is found that the combustion can be robustly stabilized over larger variation intervals of pressure parameter and time-delay parameter than those obtained in Zheng and Frank [(2002). Robust control of uncertain distributed delay systems with application to the stabilization of combustion in rocket motor chambers. Automatica, 38, 487-497].

Distributed control gains design for consensus in multi-agent systems with second-order nonlinear dynamics☆

Abstract This paper discusses the design of distributed control gains for consensus in multi-agent systems with second-order nonlinear dynamics. First, an effective distributed adaptive gain-design strategy is proposed based only on local information of the network structure. Then, a leader–follower consensus problem in multi-agent systems with updated control gains is studied. A distributed adaptive law is then proposed for each follower based on local information of neighboring agents and the leader if this follower is an informed agent. Furthermore, a distributed leader–follower consensus problem in multi-agent systems with unknown nonlinear dynamics is investigated by combining the variable structure approach and the adaptive method. Finally, simulation examples are given to illustrate the theoretical analysis.

Second-order consensus for multi-agent systems with switching topology and communication delay

In this paper, two kinds of consensus problems for second-order agents under directed and arbitrarily switching topologies are investigated, that is, the cases without and with communication delay. For the former, by constructing a new kind of digraph and employing a new graphic method, we can specify the least convergence rate for all the agents to reach consensus. For the latter, in virtue of a matrix inequality method, a sufficient condition in the form of feasible matrix inequalities is presented for all the agents to reach consensus. This, on the other hand, shows that consensus can be reached if the delay is small enough. Finally, two numerical examples are given to demonstrate the effectiveness and advantages of the proposed results.

Distributed Higher Order Consensus Protocols in Multiagent Dynamical Systems

This paper studies general higher order distributed consensus protocols in multiagent dynamical systems. First, network synchronization is investigated, with some necessary and sufficient conditions derived for higher order consensus. It is found that consensus can be reached if and only if all subsystems are asymptotically stable. Based on this result, consensus regions are characterized. It is proved that for the m th-order consensus, there are at most ⌊(m+1)/2⌋ disconnected stable and unstable consensus regions. It is shown that consensus can be achieved if and only if all the nonzero eigenvalues of the Laplacian matrix lie in the stable consensus regions. Moreover, the ratio of the largest to the smallest nonzero eigenvalues of the Laplacian matrix plays a key role in reaching consensus and a scheme for choosing the coupling strength is derived. Furthermore, a leader-follower control problem in multiagent dynamical systems is considered, which reveals that to reach consensus the agents with very small degrees must be informed. Finally, simulation examples are given to illustrate the theoretical analysis.

Passivity Analysis of Neural Networks With Time-Varying Delays

This brief considers the problem of passivity analysis for neural networks with both time-varying delays and norm-bounded parameter uncertainties. For two types of time-varying delays, delay-dependent passivity conditions are derived, respectively. These conditions are expressed in terms of linear matrix inequalities. An example is provided to show the less conservatism of the proposed conditions.

An LMI Approach to Exponential Stability Analysis of Neural Networks with Time-Varying Delay

This paper considers the problem of exponential stability analysis of neural networks with time-varying delays. The activation functions are assumed to be globally Lipschitz continuous. A linear matrix inequality (LMI) approach is developed to derive sufficient conditions ensuring the delayed neural network to have a unique equilibrium point, which is globally exponentially stable. The proposed LMI conditions can be checked easily by recently developed algorithms solving LMIs. Examples are provided to demonstrate the reduced conservativeness of the proposed results.

Filtering of Markovian Jump Delay Systems Based on a New Performance Index

This paper is concerned with the design of mode-dependent and mode-independent filters for continuous-time linear Markovian jump systems (MJSs) with time-varying delays. Different from the existing studies in the literature, the purpose of this paper is to solve the H∞, L2 - L∞ passive and dissipative filtering problems in a unified framework. This purpose is successfully realized by using a new performance index that is referred to as extended dissipativity. The extended dissipative inequality contains several weighting matrices. By tuning the weighting matrices, the extended dissipativity will reduce to the H∞ performance, L2 - L∞ performance, passivity and dissipativity, respectively. Delay-dependent conditions for the analysis of stochastic stability and extended dissipativity for MJSs with time-varying delays are obtained by using a mode-dependent Lyapunov-Krasovskii functional together with a novel integral inequality. Based on these conditions, the design methods for mode-dependent and mode-independent filters are developed based on linear matrix inequalities. The designed filters guarantee that the resulting filtering error system is stochastically stable and extended dissipative for any admissible delays. Finally, the effectiveness of the proposed methods is substantiated with three illustrative examples.