共查询到20条相似文献,搜索用时 31 毫秒
1.
Y. V. Venkatesh 《控制理论与应用(英文版)》2016,14(4):347-368
New frequency-domain criteria are proposed for the $L_2$-stability of both nonlinear single-input-single-output (SISO) and nonlinear multiple-input-multiple-output (MIMO) feedback systems, described by nonlinear integral equations. For SISO systems, the feedback block is a constant scalar gain in product with a linear combination of first-and-third-quadrant scalar nonlinearities (FATQNs) with time-delay argument functions; and, for MIMO systems, it is a constant matrix gain in product with a linear combination of vector FATQNs also with time-delay argument functions. In both the cases, the delay function in the arguments of the nonlinearities may be, in general, i) zero, ii) a constant, iii) variable-time and iv) fixed-history (only for SISO systems).
The stability criteria are derived from certain recently introduced algebraic inequalities concerning the scalar and vector nonlinearities, and involve the causal+anticausal O''Shea-Zames-Falb multiplier function (scalar for SISO systems and matrix for MIMO systems). Its time-domain $L_1$-norm is constrained by the coefficients and characteristic parameters (CPs) of the nonlinearities and, in the case of the time-varying delay, by its rate of variation also. The stability criteria, which are independent of Lyapunov-Krasovskii or Lyapunov-Razumikhin functions and do not seem to be derivable by invoking linear matrix inequalities, seem to be the first of their kind. Two numerical examples for each of SISO and MIMO systems illustrate the criteria. 相似文献
2.
An improved LMI-based approach for stability of piecewise affine time-delay systems with uncertainty
The stability problem for uncertain piecewise affine (PWA) time-delay systems is investigated in this article. It is assumed that there exists a known constant time delay in the system and the uncertainly is norm-bounded. Sufficient conditions for the stability of nominal systems and the stability of systems subject to uncertainty are derived using the Lyapunov–Krasovskii functional with a triple integration term. This approach handles switching based on the delayed states (in addition to the states) for a PWA time-delay system, considers structured as well as unstructured uncertainty and reduces the conservativeness of previous approaches. The effectiveness of the proposed approach is demonstrated by comparing with the existing methods through numerical examples. 相似文献
3.
L. Q. Thuan 《控制理论与应用(英文版)》2014,12(1):35-47
In the context of continuous piecewise affine dynamical systems and affine complementarity systems with inputs, we study the existence of Zeno behavior, i.e., infinite number of mode transitions in a finite-length time interval, in this paper. The main result reveals that continuous piecewise affine dynamical systems with piecewise real-analytic inputs do not exhibit Zeno behavior. Applied the achieved result to affine complementarity systems with inputs, we also obtained a similar conclusion. A direct benefit of the main result is that one can apply smooth ordinary differential equations theory in a local manner for the analysis of continuous piecewise affine dynamical systems with inputs. 相似文献
4.
This article addresses the problem of robust stability of piecewise affine (PWA) uncertain systems with unknown time-varying delay in the state. It is assumed that the uncertainty is norm bounded and that upper bounds on the state delay and its rate of change are available. A set of linear matrix inequalities (LMIs) is derived providing sufficient conditions for the stability of the system. These conditions depend on the upper bound of the delay. The main contributions of the article are as follows. First, new delay-dependent LMI conditions are derived for the stability of PWA time-delay systems. Second, the stability conditions are extended to the case of uncertain PWA time delay systems. Numerical examples are presented to show the effectiveness of the approach. 相似文献
5.
A discrete delay decomposition approach to stability of linear retarded and neutral systems 总被引:3,自引:0,他引:3
Qing-Long Han Author Vitae 《Automatica》2009,45(2):517-524
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. 相似文献
6.
Jun‐ichi Imura 《国际强度与非线性控制杂志
》2002,12(10):897-926
》2002,12(10):897-926
This paper presents a classification of bimodal piecewise affine systems from the viewpoint of well‐posedness. First, we address the feedback well‐posedness problem of a general class of bimodal piecewise affine systems, which is the problem of feedback equivalence to a well‐posed system. Next, based on this result, we classify all feedback well‐posed systems into four classes to address the control problem of piecewise affine systems in a systematic way. As its application, the stabilizability problem with well‐posedness is discussed for each class, and several remarks on stabilizability are given. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
7.
N. O. Sedova 《Automation and Remote Control》2012,73(10):1734-1743
New results regarding asymptotic stability of continuous systems with piecewise constant control are derived. The results are expressed in terms of the Lyapunov-Razumikhin functions, taking into account the specifics of the selected type of control. Certain illustrative examples are provided. 相似文献
8.
N. O. Sedova 《Automation and Remote Control》2012,73(9):1572-1580
New results regarding asymptotic stability of continuous systems with piecewise constant control are derived. The results are expressed in terms of the Lyapunov-Razumikhin functions, taking into account the specifics of the selected type of control. Certain illustrative examples are provided. 相似文献
9.
Recursive estimation in piecewise affine systems using parameter identifiers and concurrent learning
Piecewise affine systems constitute a popular framework for the approximation of non-linear systems and the modelling of hybrid systems. This paper addresses the recursive subsystem estimation in continuous-time piecewise affine systems. Parameter identifiers are extended from continuous-time state-space models to piecewise linear and piecewise affine systems. The convergence rate of the presented identifiers is improved further using concurrent learning, which makes concurrent use of current and recorded measurements. In concurrent learning, assumptions on persistence of excitation are replaced by the less restrictive linear independence of the recorded data. The introduction of memory, however, reduces the tracking ability of concurrent learning because errors in the recorded measurements prevent convergence to the true parameters. In order to overcome this limitation, an algorithm is proposed to detect and remove erroneous measurements at run-time and thereby restore the tracking ability. Detailed examples are included to validate the proposed methods numerically. 相似文献
10.
This paper presents sufficient conditions for the regional stability problem for switched piecewise affine systems, a special class of Hybrid Systems. This class of systems are described by an affine differential equation of the type x˙=A(δ)x+b(δ), where x denotes the continuous state vector and δ is a vector of logical variables that modifies the local model of the system in accordance with the continuous dynamics. Using a Lyapunov function of the type v(x)=x′P(x)x, we present LMI conditions that, when feasible, guarantee local stability of the origin of the switched system. Examples of switched affine systems are used to illustrate the results. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
11.
In this paper, the tracking problem for a class of discontinuous piecewise affine (PWA) systems is addressed. We propose an observer-based output-feedback control design, consisting of a feedforward, a piecewise affine feedback law and a model-based observer, solving the tracking problem. These synthesis results can also be employed to tackle the master-slave synchronisation problem for PWA systems. It is shown that for certain classes of PWA systems the design is characterised in terms of linear matrix inequalities. The results are illustrated by application to mechanical systems with discontinuous friction characteristics. 相似文献
12.
Refined Jensen-Based Multiple Integral Inequality and Its Application to Stability of Time-Delay Systems 下载免费PDF全文
Jidong Wang Zhanshan Wang Sanbo Ding Huaguang Zhang 《IEEE/CAA Journal of Automatica Sinica》2018,5(3):758-764
This paper investigates the stability of time-delay systems via a multiple integral approach. Based on the refined Jensen-based inequality, a novel multiple integral inequality is proposed. Applying the multiple integral inequality to estimate the derivative of Lyapunov-Krasovskii functional (LKF) with multiple integral terms, a novel stability condition is formulated for the linear time-delay systems. Two numerical examples are employed to demonstrate the improvements of our results. 相似文献
13.
Novel Stability Criteria for Linear Time-Delay Systems Using Lyapunov-Krasovskii Functionals With A Cubic Polynomial on Time-Varying Delay 下载免费PDF全文
One of challenging issues on stability analysis of time-delay systems is how to obtain a stability criterion from a matrix-valued polynomial on a time-varying delay. The first contribution of this paper is to establish a necessary and sufficient condition on a matrix-valued polynomial inequality over a certain closed interval. The degree of such a matrix-valued polynomial can be an arbitrary finite positive integer. The second contribution of this paper is to introduce a novel Lyapunov-Krasovskii functional, which includes a cubic polynomial on a time-varying delay, in stability analysis of time-delay systems. Based on the novel Lyapunov-Krasovskii functional and the necessary and sufficient condition on matrix-valued polynomial inequalities, two stability criteria are derived for two cases of the time-varying delay. A well-studied numerical example is given to show that the proposed stability criteria are of less conservativeness than some existing ones. 相似文献
14.
15.
Magdi S. Mahmoud 《International journal of control》2013,86(6):481-494
In this paper, we investigate a class of linear parameter-varying discrete time-delay (LPVDTD) systems where the state-space matrices depend on time-varying parameters and the delay is unknown but bounded. We treat both notions of quadratic stability based on a single quadratic Lyapunov function and affine quadratic stability using parameter-dependent Lyapunov functions. In both cases, we develop LMI-based results of stability testing for time-delay as well as delayless discrete-time systems. Then, we design state-feedback controllers which guarantee quadratic stability and an induced l 2-norm bound. For the case of dynamic output feedback control, we use a parameter-independent quadratic Lyapunov-Krasovskii function to develop LMI-based solvability conditions which are evaluated at the extreme points of the admissible parameter set. Throughout the paper, complementary results for linear parameter-varying discrete (LPVD) systems without delay are presented. 相似文献
16.
Non-Monotonic Lyapunov-Krasovskii Functional Approach to Stability Analysis and Stabilization of Discrete Time-Delay Systems 下载免费PDF全文
In this paper, a novel non-monotonic Lyapunov-Krasovskii functional approach is proposed to deal with the stability analysis and stabilization problem of linear discrete time-delay systems. This technique is utilized to relax the monotonic requirement of the Lyapunov-Krasovskii theorem. In this regard, the Lyapunov-Krasovskii functional is allowed to increase in a few steps, while being forced to be overall decreasing. As a result, it relays on a larger class of Lyapunov-Krasovskii functionals to provide stability of a state-delay system. To this end, using the non-monotonic Lyapunov-Krasovskii theorem, new sufficient conditions are derived regarding linear matrix inequalities(LMIs)to study the global asymptotic stability of state-delay systems.Moreover, new stabilization conditions are also proposed for time-delay systems in this article. Both simulation and experimental results on a p H neutralizing process are provided to demonstrate the efficacy of the proposed method. 相似文献
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18.
In this paper, we deal with the well-posedness (in the sense of existence and uniqueness of solutions) and nature of solutions for discontinuous bimodal piecewise affine systems in a differential inclusion setting. First, we show that the conditions guaranteeing uniqueness of Filippov solutions in the context of general differential inclusions are quite restrictive when applied to bimodal piecewise affine systems. Later, we present a set of necessary and sufficient conditions for uniqueness of Filippov solutions for bimodal piecewise affine systems. We also study the so-called Zeno behavior (possibility of infinitely many switchings within a finite time interval) for Filippov solutions. 相似文献
19.
This article discusses the Lyapunov-Krasovskii functional approach for the stability problem of coupled differential-functional equations. Such systems include, as special cases, many types of time-delay systems, including the lossless propagation model, some neutral time-delay systems and singular time-delay systems. After the general stability theory, the special case of coupled differential-difference equations is discussed, and the necessity for the existence of quadratic Lyapunov-Krasovskii functional is established. Discretization is used to render the stability criterion to an LMI form. 相似文献