Global output tracking control for high-order stochastic nonlinear systems with SISS inverse dynamics and time-varying delays

Xue, Lingrong; Zhang, Weihai; Lin, Yaning

doi:10.1016/j.jfranklin.2016.06.014

Cited by 25 publications

(16 citation statements)

References 23 publications

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“…Lemma (See the work of Xue et al) The following inequality holds:

{false| x + y false|}^{r} \leq c_{r} false({false| x false|}^{r} + {false| y false|}^{r} false),

where c r =1 when r <1 and

c_{r} = 2^{r - 1}

when r ≥1.…”

Section: Preliminary Resultsmentioning

confidence: 99%

“…Assumption indicates that system contains SISS‐like unmodeled dynamics. As can be seen, the ζ 0 ‐subsystem may be also concerned with all the other states x 1 ,…, x n , rather than only the state x 1 with the power of the nonlinear terms p =1 in the works of Xue et al This fact indeed adds new difficulties because more efforts should be made to the control design later. Inspired by the works of Gao et al and Sun et al, we will not use the q‐norm form here.…”

Section: Design Of State‐feedback Controller and Stability Analysismentioning

confidence: 99%

See 1 more Smart Citation

Global stabilization for a class of stochastic nonlinear systems with SISS‐like conditions and time delay

Zhang

Xue

Jiang

2018

Intl J Robust & Nonlinear

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Summary The global stabilization problem for a class of stochastic time‐delay nonlinear systems with stochastic‐input‐to‐state‐stable–like conditions is investigated. Different from the existing results, the nonlinear growing conditions are more general, and the existences of the state and input time delays make the work more challenging in the control design and stability analysis. By introducing an appropriate gain‐scaling method and using a homogeneous domain control strategy, a delay‐independent controller is constructed to ensure that the equilibrium at the origin of the closed‐loop system is globally asymptotically stable in probability. Examples are given to show the validness of the proposed method.

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“…Lemma (See the work of Xue et al) The following inequality holds:

{false| x + y false|}^{r} \leq c_{r} false({false| x false|}^{r} + {false| y false|}^{r} false),

where c r =1 when r <1 and

c_{r} = 2^{r - 1}

when r ≥1.…”

Section: Preliminary Resultsmentioning

confidence: 99%

Section: Design Of State‐feedback Controller and Stability Analysismentioning

confidence: 99%

Global stabilization for a class of stochastic nonlinear systems with SISS‐like conditions and time delay

Zhang

Xue

Jiang

2018

Intl J Robust & Nonlinear

Self Cite

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show abstract

“…On the other hand, time-delay and parametric uncertainties, which appear widely in many practical systems, may destroy stability or degrade the performance of systems [20][21][22][23][24][25][26][27][28]. Hence, it is meaningful and indispensable to explore stability for discrete-time uncertain time-delay systems governed by an infinite-state Markov chain (DUTSs-IMC).…”

Section: Introductionmentioning

confidence: 99%

Stability for discrete-time uncertain systems with infinite Markov jump and time-delay

Hou

Liu

Deng

2021

Sci. China Inf. Sci.

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In this paper, we developed a stability analysis for discrete-time uncertain time-delay systems governed by an infinite-state Markov chain (DUTSs-IMC). Some sufficient conditions for the considered systems to be exponential stability in mean square with conditioning (ESMS-C) are derived via linear matrix inequalities (LMIs), which can be examined conveniently. Under novel sufficient conditions, the equivalence among asymptotical stability in mean square (ASMS), stochastic stability (SS), exponential stability in mean square (ESMS), and ESMS-C has been established. Besides, numerical simulations are employed in result validation.

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“…For example, by employing homogeneous domination manner, the global stabilisation of stochastic time‐delay non‐linear systems with high‐order power was studied in [31] in feed‐forward form, and then, [32] discussed the finite‐time stabilisation of stochastic high‐order non‐linear systems in strict‐feedback form. Moreover, based on the adding a power integrator and the L‐K functional, the global tracking control was solved for stochastic high‐order non‐linear systems with time‐varying delay by output‐feedback [33] and adaptive design [34], respectively.…”

Section: Introductionmentioning

confidence: 99%

Global stabilisation for a class of stochastic continuous non‐linear systems with time‐varying delay

Shao

et al. 2020

IET Control Theory & Appl

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This paper studies the problem of global stabilisation for a class of continuous but non‐smooth stochastic non‐linear systems with time‐varying delays. Other than the traditional backstepping recursive control, a concise controller of the nominal system is firstly designed by employing the homogenous domination approach, which overcomes the problem of calculating explosion produced by the diffusion and Hessian terms. Then, by means of an appropriate Lyapunov–Krasoviskii functional and a design parameter, the negative effects of the time delays and non‐linear terms generated in the controller design process are dominated; the global asymptotic stability of the closed‐loop system can be ensured by the simple but effective controller, which provides significant cost savings. Finally, a simulation example is given to demonstrate the effectiveness of the presented scheme.

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Global output tracking control for high-order stochastic nonlinear systems with SISS inverse dynamics and time-varying delays

Cited by 25 publications

References 23 publications

Global stabilization for a class of stochastic nonlinear systems with SISS‐like conditions and time delay

Global stabilization for a class of stochastic nonlinear systems with SISS‐like conditions and time delay

Stability for discrete-time uncertain systems with infinite Markov jump and time-delay

Global stabilisation for a class of stochastic continuous non‐linear systems with time‐varying delay

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