Finite-Time Stability of Uncertain Nonlinear Systems with Time-Varying Delay

Hu, Jingting; Sui, Guixia; Du, Shengli; Li, Xiaodi

doi:10.1155/2017/2538904

Cited by 15 publications

(19 citation statements)

References 48 publications

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“…In Theorems and , motivated by the work of Hu et al, we have designed some controllers containing denominator Y ( t ). Next, we present some finite‐time stabilization results without denominator Y ( t ).…”

Section: Finite‐time Simultaneous Stabilizationmentioning

confidence: 99%

Finite‐time robust simultaneous stabilization of a set of nonlinear time‐delay systems

Yang

Zhang

Sun

2019

Intl J Robust & Nonlinear

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Summary This paper investigates the finite‐time robust simultaneous stabilization problem of a set of nonlinear time‐delay systems with general forms and proposes some new simultaneous stabilization results. First, by developing an equivalent form and applying augmented technique, this paper obtains an augmented equivalent form of the original systems. Secondly, based on the equivalent form, we study finite‐time simultaneous stabilization problem and present some new stabilization results by constructing some suitable Lyapunov functionals. Thirdly, using the simultaneous stabilization results obtained, this paper investigates the finite‐time robust simultaneous stabilization problem for the set systems and proposes a delay‐dependent robust simultaneous stabilization result. Finally, the study of an illustrative example shows that the results obtained by this paper work well in the finite‐time robust simultaneous stabilization the set systems. It is shown that, by using the method in this paper, the developed conditions do not contain delay terms, which can avoid solving nonlinear mixed matrix inequalities and reduce effectively computational burden in studying nonlinear time‐delay systems.

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Section: Finite‐time Simultaneous Stabilizationmentioning

confidence: 99%

Finite‐time robust simultaneous stabilization of a set of nonlinear time‐delay systems

Yang

Zhang

Sun

2019

Intl J Robust & Nonlinear

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“…The performance measure is parametrised by a weighting matrix reflecting the relative importance of the uncertainty in the initial state contrary to the uncertainty in the exogenous disturbance. When = 0, it will reduce into a sort of ∞ control with zero initial condition [25][26][27].…”

Section: Remarkmentioning

confidence: 99%

Robust Finite-Time H-Infinity Control with Transients for Dynamic Positioning Ship Subject to Input Delay

Lin

Liang

et al. 2018

Mathematical Problems in Engineering

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This paper presents the problem of robust finite-time ∞ control with transients for ocean surface vessels equipped with dynamic positioning (DP) system in presence of input delay. The main objective of this work is to design a finite-time ∞ state feedback controller, which ensures that all states of ship do not exceed a given threshold over a fixed time interval, with better robustness and transient performance subject to time-varying disturbance. Based on a novel augmented Lyapunov-Krasovskii-like function (LKLF) with triple integral terms and a method combining the Wirtinger inequality and reciprocally convex approach, a less conservative result is derived. In particular, an ∞ performance index with nonzero initial condition is introduced to attenuate the overconservatism caused by the assumption of zero initial condition and enhance the transient performance of ship subject to external disturbance. More precisely, the controller gain matrix for the DP system can be achieved by solving the linear matrix inequalities (LMIs), which can be easily facilitated by using some standard numerical packages. Finally, a numerical simulation for a ship is proposed to verify the effectiveness and less conservatism of the controller we designed.

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“…Moreover, in addition to fast convergence, the finite‐time controller has better robustness and anti‐interference ability . Therefore, many papers focus on the issue, and some methods of solving infinite‐time problem have been extended to study the finite‐time case . Authors of other works studied the finite‐time stability (FTS) and finite‐time control problem for the systems without delay.…”

Section: Introductionmentioning

confidence: 99%

“…Authors of other works studied the finite‐time stability (FTS) and finite‐time control problem for the systems without delay. Other authors developed some finite‐time control results of delay systems. Even so, the above works mainly focus on the FTS and stabilization problems of the systems with delay and without delay, and there are very few results on the finite‐time adaptive robust control topic except for the works of Chen et al, Golestani et al, Smaeilzadeh and Golestani, and Yang and Guo .…”

Section: Introductionmentioning

confidence: 99%

“…The main contributions of this paper are as follows. (1) Different from the systems studied and methods used in existing literature, the system in this paper has general form and contains time delay, uncertain and external disturbance terms simultaneously. Based on the orthogonal decomposition method and a common assumption (see Assumption in the following), we develop an equivalent form of the original system to study finite‐time adaptive robust control problem for the general nonlinear time‐delay systems.…”

Section: Introductionmentioning

confidence: 99%

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Finite‐time adaptive robust control of nonlinear time‐delay uncertain systems with disturbance

Yang

Zang

Sun

et al. 2018

Intl J Robust & Nonlinear

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This paper investigates finite-time adaptive robust control problem for a general class of nonlinear time-delay systems with uncertain and external disturbance via the Lyapunov-Krasovskii (L-K) method and presents some delay-independent and delay-dependent results on the issue. First, by applying the orthogonal decomposition method, this paper presents an equivalent form.Based on which, we study the finite-time adaptive robust control problem for the systems by constructing a specific L-K functional and designing a suitable controller. Different from existing works, this paper studies finite-time adaptive robust control problem for general nonlinear delay system and presents a delay-dependent sufficient condition on the problem. Finally, an illustrative example is given to show the effectiveness of the result in this paper. KEYWORDS finite-time adaptive robust control, L-K functional method, nonlinear time-delay uncertain system Int J Robust Nonlinear Control. 2019;29:919-934.wileyonlinelibrary.com/journal/rnc

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Finite-Time Stability of Uncertain Nonlinear Systems with Time-Varying Delay

Cited by 15 publications

References 48 publications

Finite‐time robust simultaneous stabilization of a set of nonlinear time‐delay systems

Finite‐time robust simultaneous stabilization of a set of nonlinear time‐delay systems

Robust Finite-Time H-Infinity Control with Transients for Dynamic Positioning Ship Subject to Input Delay

Finite‐time adaptive robust control of nonlinear time‐delay uncertain systems with disturbance

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