Stability Of Time-varying Systems Research Articles

Finite-time stability and stabilization for time-varying systems

This paper considers finite-time stability and stabilization for time-varying systems. By developing classical Lyapunov method, sufficient conditions are presented to guarantee the finite-time stability for more general time-varying systems that are not covered in other existing results. Estimates of the corresponding attraction domain and settling time are derived along the analysis of finite-time stability, and the proposed results are utilized in the problem of finite-time stabilization for a class of controlled systems. Two examples and their simulations are given to verify the effectiveness of the theoretical results.

Variable stiffness stability analysis based on time-domain method and experimental verification

During the turning process, if the feed rate too high, or the feed rate too large, chattering will be occurred. The variable stiffness tip can change the system stiffness during the machine work, so as to increase the limit depth, but the stability of time-varying systems is difficult to predict. This article will be explained in as follows: Firstly, in this paper, the turning stiffness is studied, and the turning dynamics model is established. Secondly, it predicts the limit depth of cut by changing the time domain model parameters, and using the variable stiffness method to optimize the ultimate depth of cut. Finally, verify the correctness of the limit depth of cut through experiments.

Strict Lyapunov Functions for Homogeneous Time-Varying Systems

We provide new criterion and a class of strict Lyapunov functions (SLFs) for time-varying systems (TVSs) with zero homogeneity. The definition of homogeneous auxiliary system is given, where it is assumed that certain homogeneous functions are admitted with their derivatives, in terms of the error systems, bounded by periodic functions. Based on the homogeneous auxiliary system, sufficient conditions of uniform asymptotical stability for TVSs are formulated using the homogeneity framework. Unlike existing results, where non-SLFs or persistence of excitation condition are required, our criterion is greatly relaxed for broad classes of systems. The utility of our result is illustrated by case-study of pendulum stability with quasi-periodical frictions.

Stability of time-varying systems in the absence of strict Lyapunov functions

Stability of time-varying systems in the absence of strict Lyapunov functions

New criterion for asymptotic stability of time-varying dynamical systems

In this paper, we establish some new sufficient conditions for uniform global asymptotic stability for certain classes of nonlinear systems. Lyapunov approach is applied to study exponential stability and stabilization of time-varying systems. Sufficient conditions are obtained based on new nonlinear differential inequalities. Moreover, some examples are treated and an application to control systems is given.

The Swing Control of Cranes with Variable Rope Length Based on Linear Time Varying System Theory

In this paper, following the state-feedback stabilization for time-varying systems proposed by Wolovich, a controller is designed for the overhead cranes with a linearized parameter-varying model. The resulting closed-loop system is equivalent, via a Lyapunov transformation, to a stable time-invariant system of assigned eigenvalues. The simulation results show the validity of this method.

Local Asymptotic Stability via Averaging for Time-Varying Systems With Unbounded Dynamics With Respect to Time

The purpose of this note is to provide sufficient conditions for asymptotic stability for time-varying systems, whose dynamics are unbounded with respect to time. An averaging approach is established that constitutes a generalization of the well known methodology adopted in the literature for systems whose dynamics are bounded with respect to time.

Division time chaos switch-synchronization for a class interrelated chaotic systems

The method of division time chaos switch-synchronization for a class of interrelated chaotic systems is proposed. The division time chaos switch-synchronization between each chaotic subsystem and its duplicate system is achieved via linear feedback control. Based on the theory of stability of time-varying systems, the range of feedback gain for synchronization of these interrelated chaotic systems is derived. Numerical simulation shows the effectiveness and feasibility of the method.

Sampled-data feedback practical semi-global controllability and stabilization for time-varying systems

We deal with the problems of the closed-loop controllability and stabilization for time-varying systems whose dynamics are in general unbounded with respect to time. It is shown that a general notion of global asymptotic controllability, being in general, non-uniform with respect to initial values of time, implies existence of a family of continuous control Lyapunov functions, and this enables the establishment of practical semi-global closed-loop controllability by means of a sampled-data time-varying feedback. Moreover, the usual concept of global asymptotic controllability, being uniform with respect to the initial values of time, implies practical semi-global stabilization by sampled-data feedback. The work is a continuation of a recent paper of the author in the same journal and extends Krichman's (2000) result relying practical stabilization of time-varying systems with bounded in time dynamics.

Coupled synchronization of the unified chaotic system

This paper investigates the synchronization of two linearly coupled unified chaotic systems. A new sufficient condition of global asymptotic synchronization is attained from the theory of stability of time-varying systems. In addition, compared with the previously proposed method, the sufficient condition for the synchronization of two linearly coupled unified chaotic systems is simpler and le ss conservative, and the range of coupled coefficients is wider. Numerical simul ation shows the effectiveness and feasibility of this method.

A Converse Lyapunov Theorem for Nonuniform in Time Global Asymptotic Stability and Its Application to Feedback Stabilization

Lyapunov-like characterizations for the concepts of nonuniform in time robust global asymptotic stability and input-to-state stability for time-varying systems are established. The main result of our work enables us to derive (1) necessary and sufficient conditions for feedback stabilization for affine in the control systems and (2) sufficient conditions for the propagation of the input-to-state stability property through integrators.

Persistent identification and adaptation: stabilization of slowly varying systems in H/sup ∞/

In this paper, the problem of persistent identification and adaptive stabilization of time-varying systems is studied within the framework of deterministic worst case identification and slow H/sup /spl infin// adaptation. The plants under consideration are unstable and time-varying and cannot be stabilized by a fixed robust controller. Starting from an initial well-designed operating point, the controller must persistently adapt to the time-varying plant to maintain uniform stability over all future time. A key property which guarantees uniform stability is that the identification-adaptation iteration satisfies a certain invariance principle. We demonstrate that the adaptive design using periodic external inputs, least squares identification, and slow H/sup /spl infin// adaptation possesses such an invariance property, leading to a successful adaptive stabilization methodology. Generic natures of our findings are discussed.

Stability of time-varying systems with adaptively estimated transfer function

It is shown that some cascade systems with all instantaneous poles lying inside the unit circle are stable. Asymptotic and exponential stability conditions are also given for systems with an adaptively estimated transfer function.

Stability of time-varying systems using a simple transformation

Stability of time-varying systems using a simple transformation

Stability of time-varying systems using a simple transformation

A frequency-domain condition for L2-stability is derived for systems with a separable non-linear time-varying (NLTV) gain in the feedback path and it is shown that the non-linearity need not lie in the first and third quadrants. For the particular case of the linear time-varying (LTV) system, its advantage over the conventional Brockett and Forys (1964) criterion is illustrated with an example.

L2-stability of time-varying systems with global conditions on the time-varying gain

The L2-stability of linear und non-linoar time-varying systems is considered and integral typo condition on the time-varying gain is obtained through the positive operator theory.

A Combined Time-Frequency Condition for Stability of Time-Varying Systems With One Nonlinearity

A means is presented for determining stability of linear time-varying systems with one feedback nonlinearity. The stability condition involves the minimization of certain time functions of the system coefficients as well as the imaginary axis behavior of a polynomial. It is required that the equation of the linear time-varying system be asymptotically stable and be in phase variable form. The nonlinearity is restricted to lie in a sector. For the limiting case of an autonomous linear system the criterion reduces to the Popov stability condition in certain cases.

On the stability of time-varying systems using an observer for feedback control†

The effects upon stability are considered when an observer is incorporated in a time-varying system to estimate the immeasurable state variables in order to implement the feedback control law.

Some remarks on the stability of time-varying systems

An illustration is presented, via examples, of the advantages and difficulties of some of the more recent techniques for the determination of stability conditions of some linear time-varying systems.

$L_2 $-Stability of Time-Varying Systems—Construction of Multipliers with Prescribed Phase Characteristics

A system consisting of a linear element $G(s)$ and a time-varying gain $n( \cdot )$ is considered. It is assumed that this system is stable for all constant gains in the sector $[0,k]$ (i.e., for $n(t) \equiv l$, $0 \leqq l \leqq k$). It is then shown that the system is stable for all $n( \cdot )$ in that sector satisfying \[\left| {\frac{1}{t}\int_0^t {} } \right|\frac{d}{{d\tau }}\left[ {\log \left( {\frac{{n(\tau )}}{{1 - {{n(\tau )} / k}}}} \right)} \right] \pm 2\sigma | {d\tau - 2\sigma } | \leqq \frac{K}{t}\] for some $K > 0$ and all $t > 0$.Here $\sigma $ is a constant determined by an equation involving (inversely) the derivative of the phase function $\arg \{ G(i\omega ) + {1 / k}\} $. The proof follows what are by now established lines in employing a “multiplier” operator. However, a method is used to eliminate any “multiplier” dependence from the final results, so that these results are explicit and geometric.