Delay-range-dependent control synthesis for time-delay systems with actuator saturation

The control synthesis problem for a class of linear time-delay systems with actuator saturation is investigated in this paper. The time delay is considered to be time-varying and has lower and upper bounds. A delay-range-dependent approach is adopted and the corresponding existence conditions of the stabilizing state-feedback controller are derived in terms of LMIs. An estimate for the domain of attraction of the origin can be obtained for the underlying systems with different time-delay ranges. Two numerical examples are presented to show the effectiveness and less conservatism of the developed theoretical results.     

Robust design of feedback integrated with iterative learning control for batch processes with uncertainties and interval time-varying delays

A robust feedback integrated with iterative learning control (FILC) scheme for batch processes with uncertain perturbations and interval time-varying delay is developed. The batch process is modeled as a two-dimensional (2D) Rosser system with a delay varying in a range. The design of FILC scheme is transformed into a robust control problem of uncertain 2D system. New delay-range-dependent stability criteria and stabilization conditions are derived in terms of linear matrix inequalities (LMIs), which depend on not only the difference between the upper and lower delay bounds but also the upper delay bound of the interval time-varying delay. Parameterized characterizations for stabilizing the controller are given in terms of the feasibility solutions to the LMIs. Applications to injection velocity control show that the proposed FILC achieve the design objectives well.     

Further improvement on delay-range-dependent stability results for linear systems with interval time-varying delays

This paper provides an improved delay-range-dependent stability criterion for linear systems with interval time-varying delays. No model transformation and no slack matrix variable are introduced. Furthermore, overly bounding for some cross term is avoided. The resulting criterion has advantages over some previous ones in that it involves fewer matrix variables but has less conservatism, which is established theoretically. Finally, two numerical examples are given to show the effectiveness of the proposed results.     

On designing memory state feedback controller for linear systems with interval time-varying delay

This paper is concerned with the design of a memory state feedback controller for linear systems with interval time-varying delays. The time delay is assumed to be a time-varying continuous function belonging to a given interval, which means that the lower and upper bounds of time-varying delay are available. First, a less conservative delayrange-dependent stability criteria is proposed by using a new interval fraction method. In the process of controller synthesis, the history information of system is considered in the controller design by introducing the lower delay state. Moreover, the usual memoryless state feedback controller for the underlying systems could be considered as a special case of the memory case. Finally, two numerical examples are given to show the effectiveness of the proposed method.     

Delay-range-dependent stability for systems with time-varying delay

This paper is concerned with the stability analysis for systems with time-varying delay in a range. An appropriate type of Lyapunov functionals is proposed to investigate the delay-range-dependent stability problem. The present results may improve the existing ones due to a method to estimate the upper bound of the derivative of Lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed Lyapunov functional, which take into account the range of delay. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.     

Robust stability criteria for uncertain linear systems with interval time-varying delay

This paper considers the robust delay-dependent stability problem of a class of linear uncertain system with interval time-varying delay and proposes less conservative stability criteria for computing the maximum allowable bound of the delay range. Less conservatism of the proposed stability criteria is attributed to the delay-central point method of stability analysis, wherein the delay interval is partitioned into two subintervals of equal length, and the time derivative of a candidate Lyapunov-Krasovskii functional based on delay decomposition technique is evaluated in each of these delay segments. In deriving the stability conditions in LMI framework, neither model transformations nor bounding techniques using free-weighting matrix variables are employed for dealing the cross-terms that emerge from the time derivative of the Lyapunov-Krasovskii functional; instead, they are dealt using tighter integral inequalities. The proposed analysis subsequently yields a stability condition in convex LMI framework that can be solved using standard numerical packages. For deriving robust stability conditions, two categories of system uncertainties, namely, time-varying structured and polytopic-type uncertainties, are considered. The effectiveness of the proposed stability criteria is validated through standard numerical examples.     

不确定切换中立时滞系统状态反馈控制器设计

研究了具有两类不确定性及区间时变时滞切换中立系统的控制器设计问题。基于平均驻留时间方法,利用分段Lyapunov-Krasovskii泛函,以线性矩阵不等式形式得到了依赖于区间时滞的控制器设计的充分条件,并且获得较小保守性结果。最后,通过仿真算例证实设计方法的有效性。     

Improved delay-range-dependent robust stability for uncertain systems with interval time-varying delay

This paper is concerned with the improved delay-range-dependent stability and robust stability criteria for linear systems with time-varying delay and norm-bounded uncertainties. In order to obtain much less conservative criteria, a Lyapunov-Krasovskii functional (LKF), which makes use of the information of both the lower and upper bounds of the interval time-varying delay, is proposed to derive new stability criteria. By using delayed decomposition approach (DDA), a tighter upper bound of the derivative of Lyapunov functional can be obtained, and thus the proposed criteria give results with less conservatism compared with some previous ones. The resulting criteria have advantages over some previous ones in that it involves fewer matrix variables but has less conservatism, which are established theoretically. We show, by four well known examples, that our result overcomes the previous allowable maximum admissible upper bound (MAUB) of the time-delay and it is less conservative than the previous results having a relatively small upper bound in the derivative of time delay.     

Improved delay-range-dependent stability criteria for linear systems with time-varying delays

This paper is concerned with the stability analysis of linear systems with time-varying delays in a given range. A new type of augmented Lyapunov functional is proposed which contains some triple-integral terms. In the proposed Lyapunov functional, the information on the lower bound of the delay is fully exploited. Some new stability criteria are derived in terms of linear matrix inequalities without introducing any free-weighting matrices. Numerical examples are given to illustrate the effectiveness of the proposed method.     

Further results on delay-range-dependent stability with additive time-varying delay systems

In this paper, new conditions for the delay-range-dependent stability analysis of time-varying delay systems are proposed in a Lyapunov–Krasovskii framework. Time delay is considered to be time-varying and has lower and upper bounds. A new method is first presented for a system with two time delays, integral inequality approach (IIA) used to express relationships among terms of Leibniz–Newton formula. Constructing a novel Lyapunov–Krasovskii functional includes information belonging to a given range; new delay-range-dependent criterion is established in term of linear matrix inequality (LMI). The advantage of that criterion lies in its simplicity and less conservative. This paper also presents a new result of stability analysis for continuous systems with two additive time-variant components representing a general class of delay with strong application background in network-based control systems. Resulting criteria are then expressed in terms of convex optimization with LMI constraints, allowing for use of efficient solvers. Finally, three numerical examples show these methods reducing conservatism and improving maximal allowable delay.