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.     

Absolute stability of the Kirchhoff string with sector boundary control

This paper addresses the stability problem of the nonlinear Kirchhoff string with nonlinear boundary control. The nonlinear boundary control is the negative feedback of the transverse velocity of the string at one end, which satisfies a sector constraint. Employing the integral type multiplier method, we establish explicit absolute exponential stability of the Kirchhoff string system.     

Absolute stability of positive systems with differential constraints

We consider discrete-time systems x(k + 1) = Ax(k) + f(x(k)) where the matrix A of the linear part is known and positive, the non-linearity f is unknown but belongs to a class for which A + f(x) is positive with spectral radius < 1 for all x Rⁿ. This, with the additional property that x - Ax - f (x) is proper, is sufficient for global stability of the system. The results are applied to the continuous system x. = Ax + B phialt(C^T x) by considering the translation operator along trajectories and studying the resulting discrete system.     

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.     

一类具有扇区非线性的时变时滞系统的绝对稳定性

讨论一类具有扇区非线性的时变时滞系统的绝对稳定性问题.基于时滞分段的思想,构造一种新的Lyapunov 泛函,进一步应用自由权矩阵结合积分不等式方法,并充分考虑时变时滞和时滞上界之间的关系,得到了基于LMI的具有更低保守性的时滞相关绝对稳定条件.最后,数值实例表明所提方法的有效性和相比已有结果的优越性.     

Absolute stability and harmonic balance

We propose an approach to finding necessary absolute stability conditions with the harmonic balance method. For systems of order two and three, these conditions are both necessary and sufficient.     

Absolute stability and integral control

Absolute stability results of both circle criterion and Popov type are derived for finite-dimensional linear plants with non-linearity in the feedback loop. The linear plant contains an integrator (and so is not asymptotically stable). The (possibly time-varying) non-linearity satisfies a particular sector condition which allows for cases with zero lower gain (such as saturation and deadzone). The conjunction of stable, but not asymptotically stable, linear plants and non-linearities with possibly zero lower gain is a distinguishing feature of the paper. The absolute stability results are invoked in proving convergence and stability properties of low-gain integral feedback control for tracking of constant reference signals in the context of exponentially stable linear systems subject to input and output non-linearities.     

不确定Lurie时滞系统绝对稳定性分析

研究了不确定Lurie时滞系统的绝对稳定问题。通过构造适当的Lyapunov泛函、引入一些自由权矩阵和充分考虑时滞导数的上限信息,得到了基于LMIs(线性矩阵不等式)形式的时滞相关绝对稳定性新准则,两个数值例子验证了所得结论的有效性和更弱保守性。     

Absolute stability analysis of PWM systems

The absolute stability, of pulse-width modulated (PWM) feedback systems with higher order linear plants is treated. The system consists of a linear, continuous plant with a piecewise-constant input from a pulse-width modulator, whose input is an error signal obtained by comparison of the plant output with the desired output. The overall system is modeled as a discrete, nonlinear feedback system. An absolute stability criterion in [4] is then used to check the stability of the system. Two effective computer algorithms are developed to find the largest possible absolute stability sectors obtainable under the sufficiency constraint of the criterion and their application is illustrated by several examples. The methods described provide the capability, to analyze higher order PWM systems in which the pole locations of the linear portion of the nonlinear feedback system are located in the negative half-plane, except for possibly one pole at the origin.     

Absolute stability via boundary control of a semilinear parabolic PDE

We consider the problem of achieving global absolute stability of an unstable equilibrium solution of a semilinear dissipative parabolic partial differential equation (PDE) through boundary control. The state space of the system is extended in order to write the action of the boundary control as an unbounded operator in an abstract evolution equation. Absolute stability via boundary control is accomplished by analyzing a control Lyapunov function based on the infinite-dimensional dynamics and applying a finite-dimensional linear quadratic regulator (LQR) controller. Sufficient conditions for absolute stability of the infinite-dimensional system are established by the feasibility of two finite-dimensional linear matrix inequalities (LMIs). Numerical results are presented for a Dirichlet boundary controlled system, however the analysis in this work applies to Nuemann and Robin type boundary controllers as well.     

Absolute stability and parameter sensitivity†

This paper extends the notion of absolute stability to include the parameter variations of the linear part of the system. A simple analytic procedure is proposed to calculate the regions of absolute stability in the parameter space. then, a parallelepiped of maximum volume is embedded in the region to interpret its boundaries and obtain readily the information about parameter variations which do not affect the system stability.     

Absolute stability analysis of linear systems with Duhem hysteresis operator

In this paper, we investigate the stability of positive and negative feedback interconnections of a linear system and a Duhem hysteresis operator. We provide sufficient conditions on the linear plant and on the Duhem operator which are based on the counterclockwise (CCW) or clockwise (CW) input–output property of the plant and hysteresis operator. We show the application of our main result in the design of a linear controller to stabilize a simple mechanical system driven by a hysteretic actuator, such as, piezo-actuator or smart material-based actuator.     

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.     

Analysis and synthesis on a generalized stability region

The generalization of the /spl nu/-gap metric to a finitely connected stability region is derived. The results hold for the class of all linear, time-invariant systems which admit a continuous coprime factorization including the nonrational case. A limited extension of the H/sub /spl infin//-loopshaping synthesis procedure is obtained via conformal mapping. An example is given where enlargement of the stability region can be used to transform the problem into one which is solvable via uniform stability margin optimization.     

Global asymptotic stability in a generalized Lotka-Volterra system

Sufficient conditions are obtained for the global asymptotic stability of a positive steady state of Lotka-Volterra systems of the form

$

when such a steady state exists and a corresponding result for an integrodifferential system is indicated.     

New delay-interval stability condition

The delay-dependent stability problem for systems with time-delay varying in an interval is addressed in this article. The new idea in this article is to connect two very efficient approaches: the discretised Lyapunov functional for systems with pointwise delay and the convex analysis for systems with time-varying delay. The proposed method is able to check the stability interval when the time-varying delay d(t) belongs to an interval [r,?τ]. The case of unstable delayed systems for r?=?0 is also treatable. The resulting criterion, expressed in terms of a convex optimisation problem, outperforms the existing ones in the literature, as illustrated by the numerical examples.     

Absolute exponential stability of a class of continuous-time recurrent neural networks

This paper presents a new result on absolute exponential stability (AEST) of a class of continuous-time recurrent neural networks with locally Lipschitz continuous and monotone nondecreasing activation functions. The additively diagonally stable connection weight matrices are proven to be able to guarantee AEST of the neural networks. The AEST result extends and improves the existing absolute stability and AEST ones in the literature.     

Absolute stability conditions for discrete-time recurrent neuralnetworks

An analysis of the absolute stability for a general class of discrete-time recurrent neural networks (RNN's) is presented. A discrete-time model of RNN's is represented by a set of nonlinear difference equations. Some sufficient conditions for the absolute stability are derived using Ostrowski's theorem and the similarity transformation approach. For a given RNN model, these conditions are determined by the synaptic weight matrix of the network. The results reported in this paper need fewer constraints on the weight matrix and the model than in previously published studies.     

Absolute stability of nonlinear systems with two additive time-varying delay components

In this paper, we present a new sufficient condition for absolute stability of Lure system with two additive time-varying delay components. This criterion is expressed as a set of linear matrix inequalities (LMIs), which can be readily tested by using standard numerical software. We use this new criterion to stabilize a class of nonlinear time-delay systems. Some numerical examples are given to illustrate the applicability of the results using standard numerical software.