On asymptotic stability of linear time-varying systems

Zhou, Bin

doi:10.1016/j.automatica.2015.12.030

Cited by 203 publications

(155 citation statements)

References 24 publications

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“…Remark From inequality in Theorem and inequality in Corollary , a conclusion can be drawn that

λ_{0} false(t false) + \frac{λ_{1} false(t false)}{β} + \frac{\log μ}{T_{a}}

and

λ_{0} false(t false) + \frac{λ_{1} false(t false)}{β}

are both UESFs with guaranteed decay rate ς . The definition of UESF was initially proposed in . It has been proved in that this concept is useful for analyzing the stability of time‐varying SDSs with impulses or without impulses.…”

Section: Resultsmentioning

confidence: 99%

“…For example, a rocket is a typical example of a time‐varying systems in which its mass will decrease with time due to fuel consumption. These systems with their characteristics changing with time are also called the variable coefficient systems . By using the Razumikhin‐type theorem, the concept of the uniformly exponentially stable function (UESF) was proposed to analyze the stability of time‐varying nonlinear systems in .…”

Section: Introductionmentioning

confidence: 99%

“…These systems with their characteristics changing with time are also called the variable coefficient systems . By using the Razumikhin‐type theorem, the concept of the uniformly exponentially stable function (UESF) was proposed to analyze the stability of time‐varying nonlinear systems in . Some excellent results about the ISS of time‐varying nonlinear systems, time‐varying nonlinear impulsive delay systems, and time‐varying nonlinear impulsive SDSs have been presented in and their cited references.…”

Section: Introductionmentioning

confidence: 99%

“…In, based on the UESF, many improved ISS criteria for time‐varying SDSs were derived. In, by using the UESF, Peng et al presented a unified Razumikhin‐type criterion on the ISS for time‐varying nonlinear impulsive time‐delay systems. To our knowledge, while using the Razumikhin‐type theorem to analyze the stability of time delay systems, it is necessary to verify the Razumikhin sufficient condition, which is not easy to accomplish.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A new unified input‐to‐state stability criterion for impulsive stochastic delay systems with Markovian switching

Chen

Shi

Lim

2019

Intl J Robust & Nonlinear

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Summary In this paper, the problems of the input‐to‐state stability (ISS), the integral input‐to‐state stability (iISS), the stochastic input‐to‐state stability (SISS) and the eλt(λ>0)‐weighted input‐to‐state stability (eλt‐ISS) are investigated for nonlinear time‐varying impulsive stochastic delay systems with Markovian switching. We propose one unified criterion for the stabilizing impulse and the destabilizing impulse to guarantee the ISS, iISS, SISS and eλt‐ISS for such systems. We verify that when the upper bound of the average impulsive interval is given, the stabilizing impulsive effect can stabilize the systems without ISS. We also show that the destabilizing impulsive signal with a given lower bound of the average impulsive interval can preserve the ISS of the systems. In addition, one criterion for guaranteeing the ISS of nonlinear time‐varying stochastic hybrid systems under no impulsive effect is derived. Two examples including one coupled dynamic systems model subject to external random perturbation of the continuous input and impulsive input disturbances are provided to illustrate the effectiveness of the theoretic results developed.

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“…Remark From inequality in Theorem and inequality in Corollary , a conclusion can be drawn that

λ_{0} false(t false) + \frac{λ_{1} false(t false)}{β} + \frac{\log μ}{T_{a}}

and

λ_{0} false(t false) + \frac{λ_{1} false(t false)}{β}

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A new unified input‐to‐state stability criterion for impulsive stochastic delay systems with Markovian switching

Chen

Shi

Lim

2019

Intl J Robust & Nonlinear

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“…However, the stability analysis of nonautonomous switched systems has been relatively less extensively studied . Liu et al proposed stability conditions for switched systems with both stable and unstable subsystems via multiple Lyapunov functions (MLF s for short) and the average dwell time based method, which required the MLF s to be nonincreasing.…”

Section: Introductionmentioning

confidence: 99%

Average dwell time based stability analysis for nonautonomous continuous‐time switched systems

She

2019

Intl J Robust & Nonlinear

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Summary Inspired by the idea of multiple Lyapunov functions and the average dwell time, we address the stability analysis of nonautonomous continuous‐time switched systems. First, we investigate nonautonomous continuous‐time switched nonlinear systems and successively propose sufficient conditions for their (uniform) stability, global (uniform) asymptotic stability, and global (uniform) exponential stability, in which an indefinite scalar function is utilized to release the nonincreasing requirements of the classical multiple Lyapunov functions. Afterwards, by using multiple Lyapunov functions of quadratic form, we obtain the corresponding sufficient conditions for (uniform) stability, global (uniform) asymptotic stability, and global exponential stability of nonautonomous switched linear systems. Finally, we consider the computation issue of our current results for a special class of nonautonomous switched systems (ie, rational nonautonomous switched systems), associated with two illustrative examples.

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Delay‐dependent conditions for finite time stability of linear time‐varying systems with delay

Chen

Sun

2019

Asian Journal of Control

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This paper investigates the problem of finite time stability of linear time‐varying system with delay. By constructing an augmented time‐varying Lyapunov functional and using the Wirtinger‐type inequality deductively, delay‐dependent finite time stability conditions are derived and presented in terms of differential linear matrix inequalities (DLMIs). Then, the DLMIs are transformed into a series of recursive linear matrix inequalities (RLMIs) by discretizing the time interval into equally spaced time distances, and an algorithm is given to solve the RLMIs. Examples illustrate the feasibility and effectiveness of the proposed method.

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On asymptotic stability of linear time-varying systems

Cited by 203 publications

References 24 publications

A new unified input‐to‐state stability criterion for impulsive stochastic delay systems with Markovian switching

A new unified input‐to‐state stability criterion for impulsive stochastic delay systems with Markovian switching

Average dwell time based stability analysis for nonautonomous continuous‐time switched systems

Delay‐dependent conditions for finite time stability of linear time‐varying systems with delay

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