Xianfu Zhang

Leader-follower consensus of upper-triangular nonlinear multi-agent systems

This paper is concerned with the leader-follower consensus problem by using both state and output feedback for a class of nonlinear multi-agent systems. The agents considered here are all identical upper-triangular nonlinear systems which satisfy the Lipschitz growth condition. First, it is shown that the leader-follower consensus problem is equivalent to the control design problem of a high-dimensional multi-variable system. Second, by introducing an appropriate state transformation, the control design problem can be converted into the problem of finding a constant parameter, which can be obtained by solving the Lyapunov equation and estimating the nonlinear terms of the given system. At last, an example is given to verify effectiveness of the proposed consensus algorithms.

Global asymptotic stabilization for input-delay chained nonholonomic systems via the static gain approach

Abstract In this paper, a novel control strategy is proposed for asymptotically stabilizing chained nonholonomic systems with input delay. Firstly, by using the input-state-scaling technique and the static gain control method, the stabilization control problem of such systems is transformed into designing two gain parameters to stabilize a class of generalized feedback systems with state delay. Then, based on the Lyapunov–Krasovskii theorem, the stability analysis of the closed-loop systems is achieved by the appropriate selection of the gain parameters, and the state and output feedback controllers are constructed simultaneously. An illustrative example is also provided to demonstrate the effectiveness of the proposed strategy.

Improved stability criteria for linear time-varying systems on time scales

ABSTRACT In this paper, asymptotic stability problems of linear time-varying (LTV) systems on time scales are considered based on a less conservative Lyapunov inequality, whose right side is not required to be necessarily negative. It is shown that the Lyapunov inequality covers not only the corresponding trivial (continuous and discrete) ones but also nontrivial ones. Based on this inequality, some necessary and sufficient conditions for asymptotic stability, exponential stability, uniformly exponential stability of LTV systems on time scales are obtained. An example about nontrivial systems is given for illustrating the effectiveness of the proposed results.

Output feedback control for a class of output-constrained nonlinear systems

This paper is concerned with the problem of output feedback stabilization for a class of output-constrained nonlinear systems that are dominated by a lower triangular system. Firstly, an observer based output feedback control scheme is proposed using the dynamic gain control design approach. Then, based on the property of Barrier Lyapunov Functions and Lyapunov stability theory, the asymptotic stability of the closed-loop system is analyzed and the output constraint is not violated. Finally, an example is given to show that the proposed design procedure is very simple and efficient.

Decentralised regulation of nonlinear multi-agent systems with directed network topologies

ABSTRACT This paper aims to address the leader–follower regulation problem of multi-agent systems with directed network topologies, where the agents are described by feedforward nonlinearities with the growth rate being unknown a priori. Both the state feedback regulation protocol and the output feedback regulation protocol are delicately constructed such that all the states of followers can converge to the leader state globally. In this paper, a model transformation is firstly performed and the leader–follower regulation problem can be transformed into a general regulation problem. Then, by introducing an appropriate state transformation, the regulation problem can be changed into a parameter determined problem. It is proved that the parameter can be determined by both the properties of M-matrices and the estimates of nonlinear terms. Finally, a numerical example is presented to show the feasibility of designed protocols.

Feedback stabilization for cross triangular nonlinear systems

This paper investigates the global asymptotic stabilization for a class of cross triangular nonlinear systems in which the nonlinearities are assumed to satisfy a linear growth condition on cross systems. The system includes both upper and lower triangular system and hence it can be seen as a generalization of triangle systems. With the help of Lyapunonv stability theorem, and the state transformation of nonlinear systems, we construct a control strategy, in which two static parameters are introduced to achieve our control purposes. A numerical example is given to illustrate the effectiveness of the proposed strategy.

Adaptive state estimation for a class of system with nonlinear parametrization

This work presents the problem of state estimation with the adaptive time-varying observer, for a class of nonlinear parameter systems in a linearly growing triangular form. The parameter appears in functions involving the unmeasured state and the bound of it is not known a priori. By extending the technology of constructing the high-gain observer, we explicitly construct an adaptive time-varying observer which converges to the system. We will present a pendulum system to show the feasibility of this technology.