Finite Time Stability and Optimal Finite Time Stabilization for Discrete-Time Stochastic Dynamical Systems

Lee, Junsoo; Haddad, Wassim M.; Lanchares, Manuel

doi:10.1109/tac.2022.3201040

Cited by 15 publications

(5 citation statements)

References 28 publications

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“…Theorem 6 (see [52]). For the system (3), assume that there exists a continuous and radially unbounded function…”

Section: Complexitymentioning

confidence: 99%

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A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control

Ran,

Zhou

2024

Complexity

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A stochastic discrete fractional Cournot duopoly game model with a unique interior Nash equilibrium is developed in this study. Some sufficient criteria of the Lyapunov stability in probability for the proposed model at the interior Nash equilibrium are derived using the Lyapunov theory. The proposed model’s finite time stability in probability is then investigated using a nonlinear feedback control approach at the interior Nash equilibrium. The stochastic Bellman theory is also used to explore the locally optimum control problem. Furthermore, bifurcation diagrams, time series, and the 0-1 test are used to investigate the chaotic dynamics of this model. Finally, numerical examples are given to illustrate the obtained results.

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“…Theorem 6 (see [52]). For the system (3), assume that there exists a continuous and radially unbounded function…”

Section: Complexitymentioning

confidence: 99%

“…Defnition 3 (see [52]). Te zero solution to the system (1) is fnite time stable if there exists a state indexed stochastic process K: D × Ω ⟶ N, called a stochastic settling-time, such that the following statements hold:…”

Section: Mathematical Preliminariesmentioning

confidence: 99%

A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control

Ran,

Zhou

2024

Complexity

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“…In recent years, FTS has been influenced and developed by the theory of linear (nonlinear) matrix inequalities, and many important contributions have emerged. Some sufficient conditions for FTS and stability of the switching system have provided [12,13]. Yang and Li extend the concept of FTS to impulse effect systems and their singular forms, and give sufficient conditions for FTS and stability problems [14].…”

Section: Introductionmentioning

confidence: 99%

Finite Time Stability Analysis Based on Dwell-Time Dependent Co-Positive Lyapunov Function

Zhang,

Liu

2024

Advances in Transdisciplinary Engineering

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Traffic signal control has always been the core problem of urban traffic control, in order to propose a more efficient signal intersection control method, this paper abstracts the signal intersection queue vehicle dissipation and waiting problem into a class of finite-time stability (FTS) problems for switching positive systems containing unstable subsystems. A new dwell-time dependent co-positive Lyapunov function (DTDCLF) is introduced, which can effectively solve the analysis of dwell-time dependent problems and can more effectively use the switching rule to construct the Lyapunov function. Sufficient conditions for the FTS of switched positive systems containing unstable subsystems in discrete-time and continuous-time contexts are obtained by this method, respectively. Lastly, an illustrative numerical example is presented to showcase the efficiency of the method. The method outlined in this paper provides a more efficient solution to the signal timing problem at oversaturated intersections, allowing vehicles at oversaturated intersections to be evacuated more quickly, reducing traffic delays and improving intersection efficiency.

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“…For NLSs having multiple unknown control directions the global FT adaptive stabilization was studied in Wu et al (2016). FT stabilization of stochastic NLSs has been discussed in Wang and Zhu (2015), Lee et al (2023), Yan et al (2015), Yin et al (2011). FT stability and stabilization of stochastic systems with Markovian switching have been investigated in Yan et al (2015).…”

Section: Introductionmentioning

confidence: 99%

Fixed-time stabilization for lower-triangular nonlinear systems under the p-normal form

Wang

2024

Transactions of the Institute of Measurement and Control

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This article investigates the fixed-time stabilization (FTS) problem for lower-triangular nonlinear systems under the [Formula: see text]-normal form. Under suitable assumptions condition of the system’s nonlinearities, a novel fixed-time partial-state feedback (PSF) control law is designed using backstepping design method and adding a power integrator (API) technique. With the help of one appropriate Lyapunov function, it is shown that the partial-state of the corresponding closed-loop system is fixed-time stable. Numerical simulation is given to illustrate the potency of the suggested continuous partial-sate feedback controller.

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Finite Time Stability and Optimal Finite Time Stabilization for Discrete-Time Stochastic Dynamical Systems

Cited by 15 publications

References 28 publications

A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control

A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control

Finite Time Stability Analysis Based on Dwell-Time Dependent Co-Positive Lyapunov Function

Fixed-time stabilization for lower-triangular nonlinear systems under the p-normal form

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