Output feedback finite‐time stabilization of a class of nonlinear time‐delay systems in the p‐normal form

Abstract

SummaryThis article investigates the finite‐time output feedback stabilization problem for a class of nonlinear time‐varying delay systems in the p‐normal form. First, a reduced‐order state observer is designed to estimate the unmeasurable state. Then, an output feedback controller is constructed, with the help of the finite‐time Lyapunov stability theorem, it is proved that the state of the resulting closed‐loop system converges to the origin in finite time. Two simulation examples are given to verify the effectiveness of the proposed scheme.

Finite-Time Stability Tools for Control and Estimation

“…As we can conclude from the results of this section, FTS is not a natural type of behavior of time-delay systems, since the influence of past values of the state may block a finite-time settling of the trajectories at the origin, then additional structural conditions are needed. Control design approaches for finite-time stabilization of time-delay systems can be found in Polyakov et al, 2015b;Nekhoroshikh et al, 2020), and the simplest ways of obtaining accelerated regulation in this class of systems is by using prediction techniques to compensate the delays as in (Karafyllis, 2006), the theory of homogeneity (Zimenko et al, 2017;Zimenko et al, 2019) or the domination approach (Wang et al, 2020b).…”

Global stabilization for a class of upper‐triangular stochastic nonlinear systems with input delay via sampled‐data output feedback

“…From the reduced-order observer (9), the coordinate transformation (10), the aforementioned constructed "virtual controller" (23) and Lemma 2, we can obtain the following inequality, for ∀s ∈ [s l , s l+1 ),…”

“…Nevertheless, for the aforementioned sampled-data literature, [5][6][7][8][9][10][11][12][13][14][15][16] they all ignored the time delays existed in the communication channels, and we should notice that time delay of data transmission is an adverse mechanism since it may seriously weaken the controller efficiency, therefore the robust investigations for the nonlinear time-delay systems have become a research topic recently. [17][18][19][20][21][22][23][24][25] Adaptive fuzzy dynamic event-triggered tracking was obtained in Reference 17 for a class of nonlinear time-delay systems with unmodeled dynamics by relying on the command filter; the robust control methods which simultaneously against time delays and actuator faults were respectively proposed in References 18-20 for the focused nonlinear systems; the decentralized stabilization and tracking were respectively reached in References 21 and 22 for the switched stochastic nonlinear time-delay systems; two finite-time stabilization and consensus strategies were respectively given in References 23 and 24 for the investigated nonlinear time-delay system and time-delay multi-agent system; a robust multi-model control method for a nonlinear time-delay system with multiple-input single-output (MISO) was proposed in Reference 25.…”

Fixed‐time output feedback stabilization of a class of high‐order planar nonlinear systems

“…1,2 During the last few years, there have been many relevant researches concerned with the finite-time output feedback stabilization of high-order nonlinear systems. In the works, [3][4][5][6][7][8][9][10][11][12][13][14] several finite-time output feedback controllers were conducted for the stabilization of high-order nonlinear systems by combining the adding a power integrator technique with auxiliary filters. In the work, 15 a simple unified finite-time output feedback controller was developed for the stabilization of uncertain high-order planar systems by utilizing the homogeneous method together with an auxiliary filter.…”