Enhancing the settling time estimation of a class of fixed‐time stable systems

• Published in: International journal of robust and nonlinear control Vol. 29; no. 12; pp. 4135 - 4148
• Main Authors: Aldana‐López, Rodrigo, Gómez‐Gutiérrez, David, Jiménez‐Rodríguez, Esteban, Sánchez‐Torres, Juan Diego, Defoort, Michael
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.08.2019; Wiley
• Subjects: Algorithms; Automatic; Computer simulation; Engineering Sciences; finite‐time stability; fixed‐time stability; Lyapunov analysis; predefined‐time stability; Rapid prototyping; Settling; Stability analysis; Upper bounds; finite-time stability; Lyapunov analysis; predefined-time stability; fixed-time stability
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.4600

Summary In this paper, we provide a new nonconservative upper bound for the settling time of a class of fixed‐time stable systems. To expose the value and the applicability of this result, we present four main contributions. First, we revisit the well‐known class of fixed‐time stable systems, to show the conservatism of the classical upper estimate of its settling time. Second, we provide the smallest constant that the uniformly upper bounds the settling time of any trajectory of the system under consideration. Third, introducing a slight modification of the previous class of fixed‐time systems, we propose a new predefined‐time convergent algorithm where the least upper bound of the settling time is set a priori as a parameter of the system. At last, we design a class of predefined‐time controllers for first‐ and second‐order systems based on the exposed stability analysis. Simulation results highlight the performance of the proposed scheme regarding settling time estimation compared to existing methods.