Sampling-interval-dependent stability for linear sampled-data systems with non-uniform sampling

This paper is concerned with the sampling-interval-dependent stability of linear sampled-data systems with non-uniform sampling. A new Lyapunov-like functional is constructed to derive sampling-interval-dependent stability results. The Lyapunov-like functional has three features. First, it depends on time explicitly. Second, it may be discontinuous at the sampling instants. Third, it is not required to be positive definite between sampling instants. Moreover, the new Lyapunov-like functional can make use of the information fully of the sampled-data system, including that of both ends of the sampling interval. By making a new proposition for the Lyapunov-like functional, a sampling-interval-dependent stability criterion with reduced conservatism is derived. The new sampling-interval-dependent stability criterion is further extended to linear sampled-data systems with polytopic uncertainties. Finally, examples are given to illustrate the reduced conservatism of the stability criteria.     

Absolute stability of sampled-data systems with a sector nonlinearity

This paper studies the absolute stability problem of sampled-data systems with a sector nonlinearity. Using the FR-operator technique, a frequency-domain criterion with a Nyquist-like plot is derived. It can be regarded as a sampled-data version of the circle criterion. It is shown that the “absolute-stability gain margin” can be read directly from the plot.     

Frequency domain stability criteria--Part II

In Part I of this paper a detailed analysis was made of the type of information Popov's Theorem gives about the stability of a closed-loop system containing a single instantaneous nonlinearity, and a new stability theorem, useful when the nonlinearity is monotone, was given. In this part a general approach for generating stability criteria is described and several specific results are obtained. In particular, an improved criterion valid whenfis an odd function is given, and criteria valid whenfis a power law nonlinearity are also developed. Several examples are included to illustrate the theory.     

Novel Stability Criteria for Sampled-Data Systems With Variable Sampling Periods

This paper is concerned with a novel Lyapunovlike functional approach to the stability of sampled-data systems with variable sampling periods. The Lyapunov-like functional has four striking characters compared to usual ones. First, it is time-dependent. Second, it may be discontinuous. Third, not every term of it is required to be positive definite. Fourth, the Lyapunov functional includes not only the state and the sampled state but also the integral of the state. By using a recently reported inequality to estimate the derivative of this Lyapunov functional, a sampled-interval-dependent stability criterion with reduced conservatism is obtained. The stability criterion is further extended to sampled-data systems with polytopic uncertainties. Finally, three examples are given to illustrate the reduced conservatism of the stability criteria.     

Frequency criteria for bounded-input--Bounded-output stability of nonlinear sampled-data systems

Sufficient conditions for absolute stability in the bounded-input-bounded-output sense are obtained for a class of nonlinear sampled-data systems. The criteria are identical to those establishing absolute stability in a global stability sense for the same class of autonomous nonlinear sampled-data systems.     

中立型时滞系统的新的绝对稳定性的法则

研究了具有扇形有界非线性的中立型时滞系统的绝对稳定性. 利用新的Lyapunov-Krasovskii泛函, 基于线性矩阵不等式得到了保守性低的稳定性结果. 从而给出了该系统的新的绝对稳定的法则. 最后用数值算例来演示所得到的结论的可行性与较低的保守性. 文中也考虑了不确定性中立型时滞系统, 他们的不确定性必须是范数有界的, 但可以是时变的.     

Robust extended dissipative control for sampled-data Markov jump systems

This paper investigates the problem of the sampled-data extended dissipative control for uncertain Markov jump systems. The systems considered are transformed into Markov jump systems with polytopic uncertainties and sawtooth delays by using an input delay approach. The focus is on the design of a mode-independent sampled-data controller such that the resulting closed-loop system is mean-square exponentially stable with a given decay rate and extended dissipative. A novel exponential stability criterion and an extended dissipativty condition are established by proposing a new integral inequality. The reduced conservatism of the criteria is demonstrated by two numerical examples. Furthermore, a sufficient condition for the existence of a desired mode-independent sampled-data controller is obtained by solving a convex optimisation problem. Finally, a resistance, inductance and capacitance (RLC) series circuit is employed to illustrate the effectiveness of the proposed approach.     

基于双边闭环函数的网络化采样控制系统稳定性分析EI北大核心CSCD

考虑数据通信时延不确定环境下网络化采样控制系统的稳定性问题.首先基于输入时滞方法,建立包含采样周期信息的网络化采样控制系统的数学模型,在此基础上,采用双边闭环函数方法和自由矩阵积分不等式技术,得到网络传输时滞变化区间依赖稳定性新准则,并进一步讨论了网络化采样控制系统中网络时延与采样周期之间的关系.仿真结果表明减小采周期可以增强网络控制系统对网络通信时延的鲁棒性.     

Frequency domain stability criteria--Part I

The objective of this paper is to illustrate the limitations of the generalized Popov Theorem in establishing the stability of a loop containing a single nonlinearity, and to use the Liapunov Theory to give a new frequency domain stability criterion for such systems. The new criterion differs from Popov's in that less restrictive assumptions are made on the linear part, and stronger assumptions are made on the nonlinearity. In this paper, it is assumed that the nonlinearity is monotone increasing. The approach used here is quite general, however, and in a companion paper various other restrictions are considered.     

基于双边闭环Lyapunov泛函的采样控制系统稳定新判据

本文研究采样控制系统的稳定性问题.通过对采样区间进行分割处理,然后,充分利用分割后的状态信息,构造了新的双边闭环型Lyapunov泛函.在界定泛函导数的过程中,通过引入新建立的系统状态方程并应用自由矩阵积分不等式方法,获得了改进的采样控制系统稳定判据.由于这样的处理方式可以捕捉到更多采样控制系统的状态信息,因而可以有效地降低稳定性分析的保守性.最后通过两个经典的数值例子对得到的稳定判据进行验证.实验结果表明,相比现有的其他方法,本文方法所得到的结论具有更小的保守性.     

Sampled-data H ∞ control for networked control systems with digital control inputs

In this article, the problem of sampled-data H _∞ control for networked control systems (NCSs) with digital control inputs is considered, where the physical plant is modelled as a continuous-time one, and the control inputs are discrete-time signals. By exploiting a novel Lyapunov–Krasovskii functional, using the Leibniz–Newton formula and a free-weighting matrix method, sufficient conditions for sampled-data H _∞ performance analysis and H _∞ controller design for such systems are given. Since the obtained conditions of H _∞ controller design are not expressed strictly in term of linear matrix inequalities, the sampled-data H _∞ controller is solved using modified cone complementary linearisation algorithm. In addition, the new sampled-data stability criteria for the NCSs is proved to be less conservative than some existing results. Numerical examples demonstrate the effectiveness of the proposed methods.     

New algebraic criteria for absolute stability of nonlinear systems

In this paper, new and simple algebraic criteria are derived via elementary proofs to provide easy sufficient conditions for the standard absolute stability problems of nonlinear systems, i.e. Lur'e problems. These criteria are equivalent to the famous graphical circle criteria and Popov criterion. By means of the Sturm theorem and the Euclidean division algorithm, a Routh-Hurwitz-like Sturm criterion is obtained. No graphical technique is needed. Only basic numerical manipulations are involved in the new criteria.     

Stability condition of a class of nonlinear feedback systems:reduction to a convex problem

This paper gives a new criterion for input-output stability of a class of nonlinear feedback systems, roughly speaking, it is most useful in such a practical situation where the nonlinearity in the system is “almost time-invariant and memoryless” but with “slight time-variations and dynamics”. It involves two free parameters and contains the circle criterion and the Popov criterion as special cases. In fact, it extends these two famous criteria in such a way that the conservatism of the circle criterion can be reduced when the time-variations and dynamics of the nonlinearity are “relatively small”. It is also shown that the existence of the free parameters that fulfil the stability condition can be checked exactly by reducing it to a convex problem in the frequency domain     

A discrete delay decomposition approach to stability of linear retarded and neutral systems

This paper is concerned with stability of linear time-delay systems of both retarded and neutral types by using some new simple quadratic Lyapunov-Krasovskii functionals. These Lyapunov-Krasovskii functionals consist of two parts. One part comes from some existing Lyapunov-Krasovskii functionals employed in [Han, Q.-L. (2005a). Absolute stability of time-delay systems with sector-bounded nonlinearity. Automatica, 41, 2171-2176; Han, Q.-L. (2005b). A new delay-dependent stability criterion for linear neutral systems with norm-bounded uncertainties in all system matrices. International Journal of Systems Science, 36, 469-475]. The other part is constructed by uniformly dividing the discrete delay interval into multiple segments and choosing proper functionals with different weighted matrices corresponding to different segments. Then using these new simple quadratic Lyapunov-Krasovskii functionals, some new discrete delay-dependent stability criteria are derived for both retarded systems and neutral systems. It is shown that these criteria for retarded systems and neutral systems are always less conservative than the ones in Han (2005a) and Han (2005b) cited above, respectively. Numerical examples also show that the results obtained in this paper significantly improve the estimate of the discrete delay limit for stability over some other existing results.     

变周期采样系统指数稳定的新条件

本文研究了线性采样系统在变周期采样下的指数稳定性问题.基于离散时间Lyapunov理论,构造了一个新的类Lyapunov泛函.该泛函不仅是时变的,还增加了对状态二次项的积分,而且不要求在采样区间内正定.利用这一新的类Lyapunov泛函,本文首先针对一类非线性采样系统提出了指数稳定性定理,再结合改进的Wirtinger积分不等式,导出了使变周期线性采样系统指数稳定以及渐近稳定的线性矩阵不等式条件.最后举例说明了所得稳定性结果比现存的某些文献报道的结果保守性较小.     

Stability analysis for a class of digital filters with single saturation nonlinearity

In this paper, a new stability criterion for a class of digital filters with single saturation nonlinearity is presented in the form of a linear matrix inequality. Numerical examples are given to show the effectiveness of the obtained results.     

Robust stability evaluation of sampled-data control systems with a sector nonlinearity in a gain-phase plane

This paper describes a graphical evaluation of the robust stability in a frequency domain based on the results from our previous paper in which the extension of Popov's criterion to discrete-time systems was expressed in an explicit form. The control system described herein is a sampled-data control system with one time-invariant nonlinear element (sector nonlinearity) in the forward path. For the purpose of application to a computer-aided control system design (CACSD), we will present an evaluation method of the robust stability in connection with the size of sector nonlinearity and the gain margin on a gain-phase diagram (i.e. a modified Nichols chart). We will show two results as numerical examples: one where Aizerman's conjecture was approved, and one where it was not. Copyright © 1999 John Wiley & Sons Ltd.     

Absolute stability of time-delay systems with sector-bounded nonlinearity

This paper deals with the problem of absolute stability of time-delay systems with sector-bounded nonlinearity. Some new delay-dependent stability criteria are obtained and formulated in the form of linear matrix inequalities (LMIs). Neither model transformation nor bounding technique for cross terms is involved through derivation of the stability criteria. Numerical examples show that the results obtained in this paper improve the estimate of the stability limit over some existing result.     

Wirtinger’s inequality and Lyapunov-based sampled-data stabilization

Discontinuous Lyapunov functionals appeared to be very efficient for sampled-data systems (Fridman, 2010, Naghshtabrizi et al., 2008). In the present paper, new discontinuous Lyapunov functionals are introduced for sampled-data control in the presence of a constant input delay. The construction of these functionals is based on the vector extension of Wirtinger’s inequality. These functionals lead to simplified and efficient stability conditions in terms of Linear Matrix Inequalities (LMIs). The new stability analysis is applied to sampled-data state-feedback stabilization and to a novel sampled-data static output-feedback problem, where the delayed measurements are used for stabilization.