scholarly journals Full-State Linearization and Stabilization of SISO Markovian Jump Nonlinear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Zhongwei Lin ◽  
Jizhen Liu ◽  
Yuguang Niu
Keyword(s):  
Nonlinear Systems ◽  
Control Design ◽  
Relative Degree ◽  
Backstepping Technique ◽  
Markovian Jump ◽  
Design Problems ◽  
Stabilizing Control ◽  
Full State ◽  
Degree Set ◽  
Coordinate Changes

This paper investigates the linearization and stabilizing control design problems for a class of SISO Markovian jump nonlinear systems. According to the proposed relative degree set definition, the system can be transformed into the canonical form through the appropriate coordinate changes followed with the Markovian switchings; that is, the system can be full-state linearized in every jump mode with respect to the relative degree setn,…,n. Then, a stabilizing control is designed through applying the backstepping technique, which guarantees the asymptotic stability of Markovian jump nonlinear systems. A numerical example is presented to illustrate the effectiveness of our results.

scholarly journals State feedback fuzzy-model-based control for Markovian jump nonlinear systems

2004 ◽  
Vol 15 (3) ◽  
pp. 279-290 ◽  
Author(s):  
Natache S. D. Arrifano ◽  
Vilma A. Oliveira
Keyword(s):  
Nonlinear Systems ◽  
Fuzzy System ◽  
System Modeling ◽  
Fuzzy Model ◽  
Control Design ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Stabilizing Controller ◽  
Model Based Control ◽  
Model Based

This paper deals with the fuzzy-model-based control design for a class of Markovian jump nonlinear systems. A fuzzy system modeling is proposed to represent the dynamics of this class of systems. The structure of the fuzzy system is composed of two levels, a crisp level which describes the Markovian jumps and a fuzzy level which describes the system nonlinearities. A sufficient condition on the existence of a stochastically stabilizing controller using a Lyapunov function approach is presented. The fuzzy-model-based control design is formulated in terms of a set of linear matrix inequalities. Simulation results for a single-machine infinite-bus power system which is modeled as a Markovian jump nonlinear system in the infinite-bus voltage are presented to illustrate the applicability of the technique.

scholarly journals Robust Adaptive Switching Control for Markovian Jump Nonlinear Systems via Backstepping Technique

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Jin Zhu ◽  
Hongsheng Xi ◽  
Qiang Ling ◽  
Wanqing Xie
Keyword(s):  
Nonlinear Systems ◽  
Controller Design ◽  
Backstepping Technique ◽  
Markovian Jump ◽  
Feedback Form ◽  
Lyapunov Stability Criterion ◽  
Small Gain ◽  
Switching Controller ◽  
Robust Adaptive ◽  
System States

This paper investigates robust adaptive switching controller design for Markovian jump nonlinear systems with unmodeled dynamics and Wiener noise. The concerned system is of strict-feedback form, and the statistics information of noise is unknown due to practical limitation. With the ordinary input-to-state stability (ISS) extended to jump case, stochastic Lyapunov stability criterion is proposed. By using backstepping technique and stochastic small-gain theorem, a switching controller is designed such that stochastic stability is ensured. Also system states will converge to an attractive region whose radius can be made as small as possible with appropriate control parameters chosen. A simulation example illustrates the validity of this method.

scholarly journals Adaptive Backstepping Control of Electrical Transmission Drives with Elastic, Unknown Backlash and Coulomb Friction Nonlinearity

2017 ◽  
Vol 26 (1) ◽  
Author(s):  
Huỳnh Văn Đông ◽  
Trần Xuân Kiên ◽  
Nguyễn Công Định
Keyword(s):  
Nonlinear Systems ◽  
Coulomb Friction ◽  
Control Design ◽  
Adaptive Controller ◽  
Uncertain Nonlinear Systems ◽  
Backstepping Technique ◽  
Adaptive Backstepping ◽  
Electrical Transmission ◽  
Adaptive Backstepping Control ◽  
Asymptotic Stable

In this paper, we present a new scheme to design an adaptive controller for uncertain nonlinear systems with unknown backlash, Coulomb friction nonlinearity. The control design is achieved by introducing a smooth approximate backlash model and certain well defined functions and by using backstepping technique. It is shown that the proposed controller can guarantee that the system is global asymptotic stable.

scholarly journals Adaptive Backstepping Control of Electrical Transmission Drives with Elastic, Unknown Backlash and Coulomb Friction Nonlinearity

2017 ◽  
Vol 26 (1) ◽  
Author(s):  
Huỳnh Văn Đông ◽  
Trần Xuân Kiên ◽  
Nguyễn Công Định
Keyword(s):  
Nonlinear Systems ◽  
Coulomb Friction ◽  
Control Design ◽  
Adaptive Controller ◽  
Uncertain Nonlinear Systems ◽  
Backstepping Technique ◽  
Adaptive Backstepping ◽  
Electrical Transmission ◽  
Adaptive Backstepping Control ◽  
Asymptotic Stable

In this paper, we present a new scheme to design an adaptive controller for uncertain nonlinear systems with unknown backlash, Coulomb friction nonlinearity. The control design is achieved by introducing a smooth approximate backlash model and certain well defined functions and by using backstepping technique. Itis shown that the proposed controller can guarantee that the system is global asymptotic stable.

Sign in / Sign up

Export Citation Format

Share Document