线性时滞广义系统的时滞相关稳定性

本文研究了线性时滞广义系统的时滞相关稳定性。首先将该系统转化为一个带约束条件的中立型系统，然后利用Lyapunov-Krasovskii V泛函方法，利用Park不等式，获得了基于LMI的时滞相关稳定充分条件，该条件具有一般性，包含正常线性时滞系统作为其特例。最后的数值例子表明所得结论较已有文献具有较小的保守性。     

Finite-Time Stability and Stabilization of Fractional Order Positive Switched Systems

This paper is concerned with finite-time stability analysis and control synthesis of fractional order positive switched systems. By using the linear copositive Lyapunov function integrated with average dwell time switching technique, the finite-time stability of fractional order positive switched systems is first addressed. Then, the finite-time boundedness of fractional order positive switched systems with exogenous input is discussed. Finally, the stabilization of the considered systems is proposed, where a control strategy based on linear programming is designed. Several implemental algorithms are provided to reduce the conservativeness of results. Two numerical examples are given to show the effectiveness of the findings of theory.     

Stability Analysis of Positive Systems With Bounded Time-Varying Delays

This brief addresses stability of the discrete-time positive systems with bounded time-varying delays and establishes some necessary and sufficient conditions for asymptotic stability of such systems. It turns out that, for any bounded time-varying delays, the magnitude of the delays does not affect the stability of these systems. In other words, system stability is completely determined by the system matrices.     

一类区间控制系统鲁棒绝对稳定性的LMI方法

本文对于区间Lurie控制系统，基于区间矩阵的等价描述和S-过程，构造了关于Lurie型Lyapunov函数中正定矩阵和积分项系数等自由参数的线性矩阵不等式(LMI)，通过LMI的解构造的Lyapunov函数来保证系统的鲁棒绝对稳定性，不必选择和调整参数。不仅讨论了无穷扇形角的情形，而且还讨论了有限扇形角的情形，所获得的结果适用于系统具有多个非线性执行机构的情形。最后给出一个实例说明本文方法的有效性，并通过实例分析了扇形角的大小与鲁棒稳定度的关系。     

Stability and Constrained Control of a Class of Discrete-Time Fuzzy Positive Systems with Time-Varying Delays

This paper deals with the stability of nonlinear discrete-time positive systems with time-varying delays represented by the Takagi–Sugeno (T–S) fuzzy model. The time-varying delays in the systems can be unbounded. Sufficient conditions of stability which are not relevant to the magnitude of delays are derived by a solution trajectory. Based on the stability results, the problems of controller design via the parallel distributed compensation (PDC) scheme are solved. The control is under the positivity constraint, which means that the resulting closed-loop systems are not only stable, but also positive. Constrained control is also considered, further requiring that the state trajectory of the closed-loop system be bounded by a prescribed boundary if the initial condition is bounded by the same boundary. The stability results and control laws are formulated as linear matrix inequalities (LMIs) and linear programs (LPs). A numerical example and a real plant are studied to demonstrate the application of the proposed methods.     

On the Asymptotic Stability of Positive 2-D Systems Described by the Roesser Model

This brief investigates the asymptotic stability of positive 2D systems described by the Roesser model. A necessary and sufficient condition is derived for the asymptotic stability, which amounts to checking the spectrum radius of the system matrix. Furthermore, it can be shown that the asymptotic stability of positive 2D systems is equivalent to that of the traditional 1D systems. This observation would greatly facilitate the analysis and synthesis of positive 2D systems.     

Stability Analysis of Switched Positive Systems: A Switched Linear Copositive Lyapunov Function Method

This brief addresses the stability problem of discrete-time switched positive systems. The main contribution lies in two aspects. First, a novel method [the switched linear copositive Lyapunov function (SLCLF)] is proposed to reduce the conservatism of the stability criterion obtained by means of the common linear copositive Lyapunov function. Second, some necessary and sufficient conditions are established for the existence of the switched linear copositive Lyapunov function, assuming that a switched linear positive system is given. A numerical example shows the advantage of the obtained results.      

Exponential Stability Criteria for Positive Systems with Time-Varying Delay: A Delay Decomposition Technique

This paper is concerned with exponential stability analysis for linear continuous positive systems with bounded time-varying delay. Our approach is based on Lyapunov–Krasovskii functional with delay decomposition. The main idea is to divide uniformly the discrete delay interval into multiple segments and then to choose proper functionals with different weighted matrices corresponding to different segments. The synthesis of our delay-dependent sufficient stability criteria is formulated in terms of linear matrix inequalities. The proposed results are shown to be less conservative compared to other results from the literature. Some illustrative examples are given to show the effectiveness of the obtained results.     

Positive Observers and Dynamic Output-Feedback Controllers for Interval Positive Linear Systems

This paper is concerned with the design of observers and dynamic output-feedback controllers for positive linear systems with interval uncertainties. The continuous-time case and the discrete-time case are both treated in a unified linear matrix inequality (LMI) framework. Necessary and sufficient conditions for the existence of positive observers with general structure are established, and the desired observer matrices can be constructed easily through the solutions of LMIs. An optimization algorithm to the error dynamics is also given. Furthermore, the problem of positive stabilization by dynamic output-feedback controllers is investigated. It is revealed that an unstable positive system cannot be positively stabilized by a certain dynamic output-feedback controller without taking the positivity of the error signals into account. When the positivity of the error signals is considered, an LMI-based synthesis approach is provided to design the stabilizing controllers. Unlike other conditions which may require structural decomposition of positive matrices, all proposed conditions in this paper are expressed in terms of the system matrices, and can be verified easily by effective algorithms. Two illustrative examples are provided to show the effectiveness and applicability of the theoretical results.      

Positive L_1 Observer Design for Positive Switched Systems

This paper investigates the problem of \(L_1\) observer design for positive switched systems. Firstly, a new kind of positive \(L_1\) observer is proposed for positive switched linear delay-free systems with observable and unobservable subsystems. Based on the average dwell time approach, a sufficient condition is proposed to ensure the existence of the positive \(L_1\) observer. Under the condition obtained, the estimated error converges to zero exponentially, and the \(L_1\) -gain from the disturbance input to the estimated error is less than a prescribed level. Then the proposed design result is extended to positive switched systems with mixed time-varying delays, where the mixed time-varying delays are presented in the form of discrete delay and distributed delay. Finally, two numerical examples are given to demonstrate the feasibility of the obtained results.     

Stabilization of Discrete-Time Positive Switched Systems

This paper addresses the stabilization for a class of discrete-time positive switched systems. Based on the average dwell time switching strategy, the stabilization of the underlying systems in the autonomous form is studied. Further, the control synthesis of non-autonomous systems is discussed. The state-feedback and output-feedback controllers are constructed, respectively. All the present conditions are solvable in terms of linear programming. Finally, four simulation examples illustrate the validity of the design.