Xiangze Lin

Brief paper: Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics

In this paper, we discuss the finite-time consensus problem for leaderless and leader-follower multi-agent systems with external disturbances. Based on the finite-time control technique, continuous distributed control algorithms are designed for these agents described by double integrators. Firstly, for the leaderless multi-agent systems, it is shown that the states of all agents can reach a consensus in finite time in the absence of disturbances. In the presence of disturbances, the steady-state errors of any two agents can reach a region in finite time. Secondly, for the leader-follower multi-agent systems, finite-time consensus algorithms are also designed based on distributed finite-time observers. Rigorous proof is given by using Lyapunov theory and graph theory. Finally, one example is employed to verify the efficiency of the proposed method.

Finite-time boundedness and L2-gain analysis for switched delay systems with norm-bounded disturbance

Abstract Finite-time boundedness and finite-time weighted L 2 -gain for a class of switched delay systems with time-varying exogenous disturbances are studied. Based on the average dwell-time technique, sufficient conditions which guarantee the switched linear system with time-delay is finite-time bounded and has finite-time weighted L 2 -gain are given. These conditions are delay-dependent and are given in terms of linear matrix inequalities. Detail proofs are given by using multiple Lyapunov-like functions. An example is employed to verify the efficiency of the proposed method.

Finite-time stability and stabilization of switched linear systems

In this paper, finite-time stability and stabilization problems for switched linear systems are discussed. Firstly, the concept of finite-time stability is extended to switched linear systems. Then, based on the state transition matrix of the system, a necessary and sufficient condition for finite-time stability of switched linear systems is presented. For ease of reference, some sufficient conditions under which the switched linear systems are finite-time stable and uniformly finite-time stable are given by virtue of matrix inequalities. Moreover, stabilizing state feedback controllers and a class of switching signals with average dwell-time are designed in detail to solve finite-time stabilization problem. The main results are proved by using the multiple Lyapunov-like functions and common Lyapunov-like function respectively. Finally, two examples are employed to verify the efficiency of the proposed method.

Finite-time stability of switched nonlinear systems with finite-time unstable subsystems

Abstract Up to now, the precondition that each subsystem should be finite-time stable or finite-time bounded is potentially assumed in most existing results for finite-time stability and finite-time boundedness of switched systems. If one subsystem of switched systems is not finite-time stable or finite-time bounded, the previous results may not work. In this paper, based on Lyapunov-like functions, finite-time stability and finite-time boundedness problems of switched nonlinear systems with subsystems that are not finite-time stable or finite-time bounded are discussed. Sufficient conditions are given under which switched nonlinear systems with subsystems that are finite-time unstable or finite-time unbounded are guaranteed to be still finite-time stable or finite-time bounded by virtue of Lyapunov-like functions respectively. The results also show the effect of switching signals and the total dwell time of finite-time unstable or finite-time unbounded subsystems on finite-time stability and finite-time boundedness of switched nonlinear systems. Numerical examples are employed to verify the efficiency of the proposed method.

Finite-time boundedness for switched systems with sector bounded nonlinearity and constant time delay

Finite-time boundedness and finite-time stability of switched systems with sector bounded nonlinearity and constant time delay are investigated. Sufficient conditions which guarantee finite-time stability or finite-time boundedness of the switched nonlinear system are presented respectively. Average dwell time of switching signals is also given. Moreover, finite-time weighted L2-gain of the switched nonlinear system is addressed to measure its disturbance tolerance capability in the fixed time interval. Detail proofs are accomplished by using multiple Lyapunov-like functions. An example is employed to verify the efficiency of the proposed method.

Finite-time stabilization of switched linear systems with nonlinear saturating actuators

Abstract In this paper, finite-time stabilization of switched linear systems with saturating actuators is discussed by virtue of time domain approach. State feedback controllers are designed to make the closed-loop systems finite-time stable. If the state is unavailable, observer-controller compensators are used. The results not only give sufficient conditions for finite-time stabilization of switched linear systems with saturating actuator, but also show the effect of the switching signals on finite-time stabilization of the system. Moreover, based on average dwell-time technique, we present the average dwell-time of switching signals to guarantee finite-time stability of the closed loop system. An example is employed to verify the efficiency of the proposed method.

Smooth output feedback stabilization of a class of planar switched nonlinear systems under arbitrary switchings

Abstract Smooth output feedback stabilization problem for a family of planar switched nonlinear systems is addressed. First, based on the adding a power integrator technique, the tasks of finding a common Lyapunov function and designing state feedback stabilizing control laws are accomplished simultaneously. Then, combining the state feedback control laws and the reduced-order nonlinear observers, output feedback control laws are designed to globally stabilize the switched nonlinear system under arbitrary switchings, whose subsystems may have uncontrollable/unobservable Jacobian linearizations.

Finite-time stabilization of switched linear time-delay systems with saturating actuators

In this paper, finite-time stabilization of switched linear time-delay systems with saturating actuators is addressed. State feedback controllers are presented to make the closed-loop systems finite-time stable. Not only the gain matrix of the saturating actuator but also the switching signal is designed to guarantee the finite-time stability of the switched systems. Sufficient conditions for both delay independent and delay dependent cases are given. The results in this paper which are expressed by scalar inequalities show the transient performance of the controlled switched systems. The bound of the trajectory given by the proposed methods leads us easily to judge the finite-time stability of the closed-loop switched systems. An example is employed to verify the efficiency of the proposed method.

Set finite-time stability of a class of switched systems

Finite-time stability of a class of switched systems is discussed. First, the definition of set finite-time stability of switched systems is proposed, and sufficient conditions under witch switched systems is finite-time stable are also given. Finite-time stability results are proved by using common Lyapunov-like function and multiple Lyapunov-like functions respectively. Moreover, based on the proposed method, output finite-time stability of a class of switched linear systems is discussed. An example is employed to verify the proposed method.

Finite Time Set Stabilization of Chua's Chaotic System

In this paper, set stabilization problem of the closed loop Chuas chaotic system is solved by using finite time control techniques. We show that the closed loop Chuas chaotic system is globally stabilized at an invariant set which consists of its equilibria in finite time. Simulation results are presented to verify our method.