Finite‐time stabilization for a class of switched stochastic nonlinear systems with dead‐zone input nonlinearities

Abstract

Summary This paper studies the finite‐time stabilizing control problem for a class of switched stochastic nonlinear systems (SSNSs) in p‐normal form. The switched systems under consideration possess the powers of different positive rational numbers and the dead‐zone input nonlinearities. Based on the improving finite‐time stability theorem for SSNSs established in this paper, a general framework to address common state feedback for SSNSs is developed by adopting the common Lyapunov function–based adding a power integrator technique. It is proved that the proposed controller renders the trivial solution of the closed‐loop system uniformly finite‐time stable in probability under arbitrary switchings. Finally, simulation results are given to confirm the validity of the proposed approach.

Output feedback stabilization of time‐delay nonlinear systems with unknown continuous time‐varying output function and nonlinear growth rate

“…On the other hand, the controlled system is usually affected by various types of uncertain factors, and one can consult References for the manipulation of unknown parameters and external disturbances. It is worth noticing that expensive sensors, physical difficulties, and effects of noises could make some state variables unapplicable, so the designer has to reconstruct them appropriately, where the systematic methodology can be found in the books .…”

Output feedback stabilization for nonholonomic systems with unknown unmeasured states‐dependent growth

“…Remark In the case of , the uncertain nonholonomic system degenerates into a driftless chained‐form nonholonomic system proposed in the work of Murray and Sastry . In literature, the extensions such as nonlinear drifts, the time‐delayed case, stochastic noise, and consensus control, are discussed for such class of uncertain nonholonomic systems. Throughout this paper, we make the following assumption regarding system .…”

Adaptive finite‐time tracking control for output‐constrained nonlinear systems with non‐strict‐feedback structure

“…On the base of the Lyapunov stability theory in References and , the finite‐time stability issues of nonlinear systems were discussed by many authors . Among them Lv et al and Liu et al designed the control programs for a class of nonlinear systems with hysteretic characteristics Wang et al, Chen et al and Yang et al discussed the finite‐time stability of time‐varying delay systems by adopting more appropriate Lyapunov‐Krasovskii functional Wang et al and Liu et al proposed the finite‐time control schemes for the nonlinear system with actuator failures Liu et al, Gao et al and Li et al investigated several finite‐time tracking control schemes for a class of nonlinear systems with dead‐zone, Wang et al and Zhang et al proposed the adaptive finite‐time control design schemes for a kind of nonlinear quantized systems. It should be noted that the above work does not consider the case where the system output is constrained.…”

“…In addition, in comparison with the current literatures on constrained systems, a series of finite‐time control schemes were constructed in References . The control strategies in References cannot ensure that the tracking error always stays in the prescribed proper range. To prevent the violation of output constraints, BLF is used in this article to ensure that the system output is constrained within a specified area and the tracking error remains in a prescribed appropriate bound.…”