Input-output finite-time stability of time-varying linear singular systems

This paper studies the input-output finite-time stabilization problem for time-varying linear singular systems. The output and the input refer to the controlled output and the disturbance input,respectively.Two classes of disturbance inputs are considered,which belong to L-two and L-infinity.Sufficient conditions are firstly provided which guarantee the input-output finite-time stability.Based on this,state feedback controllers are designed such that the resultant closed-loop systems are input-output finite-time stable.The conditions are presented in terms of differential linear matrix inequalities.Finally,an example is presented to show the validity of the proposed results.     

Chattering free full-order sliding-mode control

In conventional sliding-mode control systems, the sliding-mode motion is of reduced order. Two main problems hindering the application of the sliding-mode control are the singularity in terminal sliding-mode control systems and the chattering in both the conventional linear sliding-mode and the terminal sliding-mode control systems. This paper proposes a chattering-free full-order terminal-sliding-mode control scheme. Since the derivatives of terms with fractional powers do not appear in the control law, the control singularities are avoided. A continuous control strategy is developed to achieve the chattering free sliding-mode control. During the ideal sliding-mode motion, the systems behave as a desirable full-order dynamics rather than a desirable reduced-order dynamics. A systematic design method of full-order sliding-mode control for nonlinear systems is presented, which allows both the chattering and singularity problems to be resolved. Simulations validate the proposed chattering free full-order sliding-mode control.     

Finite-time coordination in multiagent systems using sliding mode control approach

Finite-time stability in dynamical systems theory involves systems whose trajectories converge to an equilibrium state in finite time. In this paper, we use the notion of finite-time stability to apply it to the problem of coordinated motion in multiagent systems. Specifically, we consider a group of agents described by fully actuated Euler–Lagrange dynamics along with a leader agent with an objective to reach and maintain a desired formation characterized by steady-state distances between the neighboring agents in finite time. We use graph theoretic notions to characterize communication topology in the network determined by the information flow directions and captured by the graph Laplacian matrix. Furthermore, using sliding mode control approach, we design decentralized control inputs for individual agents that use only data from the neighboring agents which directly communicate their state information to the current agent in order to drive the current agent to the desired steady state. Sliding mode control is known to drive the system states to the sliding surface in finite time. The key feature of our approach is in the design of non-smooth sliding surfaces such that, while on the sliding surface, the error states converge to the origin in finite time, thus ensuring finite-time coordination among the agents in the network. In addition, we discuss the case of switching communication topologies in multiagent systems. Finally, we show the efficacy of our theoretical results using an example of a multiagent system involving planar double integrator agents.     

Non-existence of finite-time stable equilibria in fractional-order nonlinear systems

We note that in the literature it is often taken for granted that for fractional-order system without delays, whenever the system trajectory reaches the equilibrium, it will stay there. In fact, this is the well-known phenomenon of finite-time stability. However, in this paper, we will prove that for fractional-order nonlinear system described by Caputo’s or Riemann–Liouville’s definition, any equilibrium cannot be finite-time stable as long as the continuous solution corresponding to the initial value problem globally exists. In addition, some examples of stability analysis are revisited and linear Lyapunov function is used to prove the asymptotic stability of positive fractional-order nonlinear systems.     

混沌和超混沌系统的自适应有限时间投影同步

在混沌系统投影同步的研究中,针对驱动-响应系统达到投影同步的时间不确定问题,提出了一种可以预先计算出同步时间,且在此时间内混沌系统实现投影同步的方法.对给定的驱动系统,构造合适的响应系统;采用自适应控制法,仅在误差系统的部分状态变量上加入自适应控制器;采用李亚普诺夫稳定性理论证明了在所采用的自适应控制律作用下,误差系统稳定同时驱动-响应系统达到有限时间投影同步.以典型的统一混沌系统和超混沌系统进行了数值仿真,结果进一步验证了上述控制方法的有效性与可行性.     

Semi-global finite-time observers for nonlinear systems

It is well known that high gain observers exist for single output nonlinear systems that are uniformly observable and globally Lipschitzian. Under the same conditions, we show that these systems admit semi-global and finite-time converging observers. This is achieved with a derivation of a new sufficient condition for local finite-time stability, in conjunction with applications of geometric homogeneity and Lyapunov theories.     

基于LMI的大型互联线性系统的分散有限时间镇定

借助于有限时间稳定性的定义,针对大型互联线性系统,引入了分散有限时间镇定的概念.对一类大型互联线性系统进行分散状态反馈和分散动态输出反馈控制器设计,利用线性矩阵不等式(LMI)的方法提出一个充分条件,当反馈控制律作用于该系统时,闭环系统是有限时间稳定的.仿真算例说明了所得结论的可行性和有效性.     

Finite-time stability and stabilisation of singular discrete-time linear positive systems with time-varying delay

ABSTRACT

In this paper, the problem of finite-time stability and stabilisation for positive singular discrete-time linear systems with time-varying delay is investigated. We first present novel delay-dependent sufficient conditions for positivity and finite-time stability of the unforced systems. We then apply the obtained results to solve finite-time stabilisation problem of the considered systems. The sufficient conditions for the positivity and finite-time stabilisable of such systems are formulated in terms of a standard linear programming (LP) problem. Numerical examples are provided to illustrate the effectiveness and advantages of our results.