Semi-Global Predefined-Time Stable Vector Systems

Jiménez‐Rodríguez, Esteban; Sánchez‐Torres, Juan Diego; Loukianov, Alexander G.

doi:10.1109/cdc.2018.8619355

Cited by 5 publications

(2 citation statements)

References 17 publications

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“…Remark 3: By considering a design method of semi-global predefined-time system in [9,10,20]. A class of candidate Lyapunov function can be set as:…”

Section: A Second-order Systemmentioning

confidence: 99%

“…However, the upper bound of the settling time of traditional fixed-time is usually determined by two or more parameters, hence, a simplifying fixed-time stability system is presented in [8] to make the upper bound of settling time explicit in the system function. In addition, the improved fixed-time stability system can also obtain an upper bound of settling time without enlarging and reducing mathematically [9,10], but most of traditional fixed-time stability systems enlarged the upper bound of settling time. Especially, a note on predefined-time stability in [11] pointed that the predefined-time stability of system can be guaranteed without the exponential term.…”

Section: Introductionmentioning

confidence: 99%

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On Parameter Selection of Nonsingular Predefined-time Terminal Sliding Mode With the Fixed-time Convergence Guarantee

Yan

2020

Preprint

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This paper study the parameter selection of predefined-time sliding mode and try to design a general nonsingular predefinedtime terminal sliding mode. 1). On parameter selection: Some existing predefined-time sliding modes are designed to focus on the reaching time and ignore the characterization of the equilibrium point i.e. xe = 0. In actual engineer, the system can only converge to a small neighborhood near the equilibrium point because of the existence of uncertainty i.e. xe → 0. The actual equilibrium point should be deduced by taking the limit but not directly solve the equilibrium point. Hence, the actual selection of exponential term is suggested to be not 1 to make system convergence to the equilibrium point within predefined time.2). On singularity-avoidance: Based on the exponential feature of predefined-time stability systems, a mathematic concept of switching sliding mode [1] is applied in the design of nonsingular predefined-time terminal sliding mode. However, this class of sliding mode switching method will cause a singular problem, which can be described as control input u → ∞ if the system state x → 0 and any-order time derivative of x is not 0. Hence, a non-singular selection condition for each recursive sliding mode surface is explored in this paper to realize the global finiteness of control input. In addition, an unnecessary chattering of control input will also be caused by the sliding mode switching frequency, and a novel switching condition will be applied in the controller to reduce this chattering. Simulations will be carried out to validate the effect of the novel nonsingular predefined-time sliding mode control method to some extent.

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“…Remark 3: By considering a design method of semi-global predefined-time system in [9,10,20]. A class of candidate Lyapunov function can be set as:…”

Section: A Second-order Systemmentioning

confidence: 99%