A class of predefined-time stable dynamical systems

By J. D. Sánchez-Torres, D. Gómez‐Gutiérrez, Esteban López, Alexander Georgievich Loukianov. 2018

521 citations recorded by the source corpus.

This article introduces predefined-time stable dynamical systems which are a class of fixed-time stable dynamical systems with settling time as an explicit parameter that can be defined in advance. This concept allows for the design of observers and controllers for problems that require to fulfil hard time constraints. An example is encountered in the fault detection and isolation problem, where mode detection in a timely manner needs to be guaranteed in order to apply a recovery action. Furthermore, through the notion of strong predefined-time stability, the approach hereinafter presented permits to overcome the problem of overestimation of the convergence time bound encountered in previous methods for the analysis of finite-time stable systems, where the stabilization time is often an unbounded function of the initial conditions of the system. A Lyapunov analysis is provided together with a detailed discussion of the applications to consensus and first order sliding mode controller design.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/1c82b9d0255c11e80d5b9f4610d74c5af0fac5a8

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In Control and Systems Engineering

Citations in the corpus

Prescribed-Time Control and Its Latest Developments (2022, methodology): “Proposition 9 [93]: For system ẋ = f (x, t), if there exists a C1 function V(x) ≥ 0 such that”
Adaptive Prescribed-Time Control for a Class of Uncertain Nonlinear Systems (2022, background): “Lately, the problem of preset the upper bound of the settling time in fixed-time stabilization, which can be referred as the predefined-time stabilization problem, was studied in [22]–[24].”
Predefined-Time Robust Stabilization of Robotic Manipulators (2019, background): “vanced notion named predefined-time stability, which has been investigated in [10].”
A Lyapunov-Like Characterization of Predefined-Time Stability (2019, methodology): “To overcome this mentioned drawback, it is necessary to consider another class of dynamical systems that exhibit the property of predefined-time stability, which has been studied in [9] and [10].”