In this paper, global adaptive finite-time stabilization is investigated by logic-based switching control for a class of uncertain nonlinear systems with the powers of positive odd rational numbers. Parametric uncertainties entering the state equations nonlinearly can be fast time-varying or jumping at unknown time instants, and the control coefficient appearing in the control channel can be unknown. The bounds of the parametric uncertainties and the unknown control coefficient are not required to know a priori. Our proposed controller is a switching-type one, in which a nonlinear controller with two parameters to be tuned is first designed by adding a power integrator, and then a switching mechanism is proposed to tune the parameters online to finite-time stabilize the system. An example is provided to demonstrate the effectiveness of the proposed result.

This paper investigates the state observer design of a class of unknown input switched linear systems via mode-dependent dwell time switchings. The distinguishing feature of the proposed method is that strong detectability condition of subsystems of the switched systems is unnecessarily required. First, a time-varying coordinate transformation is introduced to design a suitable reduced-order observer for each subsystem. Then, computable sufficient conditions on the synthesis of the observers are proposed in the framework of a mode-dependent dwell time technique. Since the observer of an individual subsystem cannot be designed due to unavailability of strong detectability condition of the subsystem, the state of the switched system is estimated under the condition of confining the dwell time by a pair of upper and lower bounds, restricting the growth of the Lyapunov function of the active subsystem and forcing “energy” of the overall switched system to decrease at switching instants. Finally, an example is presented to demonstrate the effectiveness of the proposed method.

This paper investigates standard H _∞ control of switched systems via dwell-time switchings without posing any internal stability requirements on subsystems of the switched systems. First, a sufficient condition is formed by specifying lower and upper bounds of the dwell time, constraining upper bound of derivative of a Lyapunov function of the active subsystem, and forcing the Lyapunov function values of the overall switched system to decrease at switching times to achieve standard H _∞ control of unforced switched linear systems. Then, in the same framework of the dwell time, sufficient conditions are given for that of the corresponding forced switched linear systems by further designing state feedback controllers. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed results.

This paper is concerned with the global finite-time stabilisation problem for a class of switched nonlinear systems under arbitrary switchings. All subsystems of the studied switched system under consideration are in lower triangular form. Based on the adding one power integrator technique, both a class of non-Lipschitz continuous state feedback controllers and a common Lyapunov function are simultaneously constructed such that the closed-loop switched system is global finite-time stable under arbitrary switchings. In the controller design process, a common coordinate transformation of all subsystems is exploited to avoid using individual coordinate transformations for subsystems. Finally, two examples are given to show the effectiveness of the proposed method.

This article deals with the global robust stabilisation for a class of switched nonlinear systems under arbitrary switchings. The system under consideration is in lower triangular form and contains uncertainty. Both common Lyapunov function and state feedback controller are simultaneously constructed by backstepping such that the closed-loop system is globally robustly asymptotically stable under arbitrary switchings. Lastly, the design method proposed is extended to the uncertain switched nonlinear systems in nested lower triangular form to solve the global robust stabilisation problem under arbitrary switchings. Two examples are given to show the effectiveness of the proposed methods.

This article investigates the exponentially stabilization problem for a class of switched positive systems with actuator saturation under dwell time switching signal. The state feedback controllers for each subsystem are designed by proposing a new type of multiple time-varying linear co-positive Lyapunov functions (MTVLCLFs), and sufficient conditions for the exponentially stabilization of the studied systems are proposed under dwell-time switching. In order to cope with actuator saturation, the convex hull technique is utilized. Finally, an example of a turbofan engine model is presented to show the effectiveness of our proposed method.