Abstract
New control procedures for finite-time stabilization of discrete-time nonlinear systems in the strict-feedback form are proposed. The proposed designs enjoy the properties of being dependent on one design parameter and the ability to bring the state vector to the origin in finite time. Moreover, the settling-time functions are estimated in terms of the initial state vector and the unique design parameter that regulates the rate of the finite-time convergence. Finally, a trajectory-tracking control algorithm is presented and approved by numerical simulations. The simulation results have shown the excellent performance of the closed-loop system for different values of the free design parameter.
Highlights
Asymptotic stability is a minimal requirement to steer the states of dynamical systems to zero when time elapses
The global finite-time stability of a class of uncertain nonlinear systems in strict-feedback form is considered in [13] where C(1) non-Lipschitz feedback is conceived to make the system globally finite-time stable. As it has been reported in [4], the global finite-time stability can be assured if the derivative of the proper Lyapunov function V (x) along the trajectories of the system is less than −c V α(x) where 0 < α < 1 and c > 0
The efficiency of the control designs are testified through illustrative examples
Summary
Asymptotic stability is a minimal requirement to steer the states of dynamical systems to zero when time elapses. The global finite-time stability of a class of uncertain nonlinear systems in strict-feedback form is considered in [13] where C(1) non-Lipschitz feedback is conceived to make the system globally finite-time stable As it has been reported in [4], the global finite-time stability can be assured if the derivative of the proper Lyapunov function V (x) along the trajectories of the system is less than −c V α(x) where 0 < α < 1 and c > 0. In contrast to the back-stepping control design proposed in [32], the algorithm proposed ensures finite-time stability by acting on one design parameter that regulates the rate of convergence to the absolute zero or to a small neighborhood of the origin. The paper is enhanced by illustrative examples that highlight the efficacy, the simplicity and the main features of the proposed designs
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
