Ruicheng Ma

Brief paper: Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings

This paper is concerned with the global stabilization problem for switched nonlinear systems in lower triangular form under arbitrary switchings. Two classes of state feedback controllers and a common Lyapunov function (CLF) are simultaneously constructed by backstepping. The first class uses the common state feedback controller which is independent of switching signals; the other class utilizes individual state feedback controllers for the subsystems. As an extension of the designed method, the global stabilization problem under arbitrary switchings for switched nonlinear systems in nested lower triangular form is also studied. An example is given to show the effectiveness of the proposed method.

Global finite-time stabilization of a class of switched nonlinear systems with the powers of positive odd rational numbers

In this paper, we will present new results on global finite-time stabilization for a class of switched strict-feedback nonlinear systems, whose subsystems have chained integrators with the powers of positive odd rational numbers (i.e., numerators and denominators of the powers are all positive odd integers but not necessarily relatively prime). All the powers in each equation of subsystems of the switched systems can be different. Based on the technique of adding a power integrator, the global finite-time stabilizers of individual subsystems are first systematically constructed to guarantee global finite-time stability of the closed-loop smooth switched system under arbitrary switchings, and then a co-design of stabilizers and a state-dependent switching law is proposed to achieve global finite-time stabilization of the closed-loop non-smooth switched systems. In the controller design, a common coordinate transformation of all subsystems is exploited to avoid using individual coordinate transformations for individual subsystems. We also give some sufficient conditions that enable our design by characterizing the powers of the chained integrators of the considered switched systems. Numerical examples are provided to demonstrate the effectiveness of the proposed results.

Backstepping design for global robust stabilisation of switched nonlinear systems in lower triangular form

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.

Global finite-time stabilisation of a class of switched nonlinear systems

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.

Global robust stabilisation of a class of uncertain switched nonlinear systems with dwell time specifications

This paper is concerned with the global robust stabilisation problem for a class of uncertain switched nonlinear systems in lower triangular form under any switching signal with dwell time specifications. The switched systems under consideration allow the uncertainties to appear in the system. We first design two classes of controllers containing a tuning gain. One designed by backstepping is related to a global convergence with respect to a compact set and the other with gain-scaling factor characters a local asymptotic stable toward the origin. A controller selection mechanism is then introduced to determine which class of controller is employed based on the compact set. The gain tuning mechanism related to the dwell time is then proposed to tune online the controller gain. It is shown that under our proposed control strategy, the global robust stability of the closed-loop switched system is achieved with the dwell time specifications. Finally, simulation results are presented to demonstrate the effectiveness of the proposed approach.

Robust state feedback stabilization of uncertain switched linear systems subject to actuator saturation

This paper addresses the robust stabilization problem for a class of switched linear systems affected by time-varying uncertainties with saturating actuators. The objective is to design a switching law and a state feedback control law such that the closed-loop system is asymptotically stable at the origin with a large domain of attraction. Via the multiple Lyapunov functions method, sufficient conditions for robust stabilization are derived. If some scalars parameters are selected in advance, the state feedback control law and the estimation of domain of attraction are presented by solving a convex optimization problem with LMI constraints. A numerical example is given to show the effectiveness of the proposed method.

Finite-time stabilization of a class of output-constrained nonlinear systems

Abstract This paper is concerned with the finite-time stabilization with output constraint for a class of uncertain nonlinear systems. The systems under consideration admit a structure which includes the one dominated by lower triangular form as a special case. We give some sufficient conditions that enable our design by characterizing the nonlinear functions of the considered systems. Based on the technique of adding one power integrator, both the finite-time stabilizers and the Barrier Lyapunov function are systematically constructed to guarantee finite-time stability of the closed-loop smooth switched system while the output constraint is not violated in a domain. An example is provided to demonstrate the effectiveness of the proposed result.

Adaptive Finite-Time Stabilization of a Class of Uncertain Nonlinear Systems via Logic-Based Switchings

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.

Dwell-time-based stabilization of switched linear singular systems with all unstable-mode subsystems

Abstract The global stabilization design of a class of switched linear singular systems via a novel dwell-time switching is investigated and solved in this work. The distinguishing feature of the proposed method is that stability of all subsystems of the switched systems is not necessarily required. A time-varying coordinate transformation is introduced first in order to convert the problem into an equivalent one of reduced-order switched conventional linear system with state jumps. Then, by constructing certain new multiple time-varying Lyapunov functions, computable sufficient conditions for the global stabilization task are proposed within the framework of dwell-time switching. Given the assumed instability of individual subsystems, the stabilization of the switched system is achieved under the condition of confining the dwell time by a certain pair of upper and lower bounds, which restrict the growth of Lyapunov function for the actively operating subsystem, thus decrease the energy of the Lyapunov function of the overall switched system at switching times. In addition, the multiple time-varying Lyapunov functions method is also used to analyze the stability analysis of a class of switched linear singular systems with stable subsystems. Two illustrative examples are presented to demonstrate the effectiveness of the proposed method.

Dwell-Time-Based Observer Design for Unknown Input Switched Linear Systems Without Requiring Strong Detectability of Subsystems

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.