Technical Briefs

Global Output Feedback Stabilization of a Class of Nonlinear Systems With Multiple Output

[+] Author and Article Information
Chunjiang Qian

Department of Electrical and Computer Engineering,
The University of Texas at San Antonio,
1 UTSA Circle,
San Antonio, TX 78249
e-mail: chunjiang.qian@utsa.edu

Qi Gong

Department of Applied Mathematics and Statistics,
Baskin School of Engineering,
University of California,
Santa Cruz, CA 95064
e-mail: qigong@soe.ucsc.edu

Roughly speaking, the solutions of a system are said to be finite-time stable if the solutions are stable and will reach the origin in a finite time and stay there afterwards. A more precise definition can be found in the references [2,7].

Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Dynamic Systems, Measurement and Control. Manuscript received February 10, 2012; final manuscript received March 7, 2013; published online May 15, 2013. Assoc. Editor: Eugenio Schuster.

J. Dyn. Sys., Meas., Control 135(4), 044502 (May 15, 2013) (6 pages) Paper No: DS-12-1054; doi: 10.1115/1.4024000 History: Received February 10, 2012; Revised March 07, 2013

This paper considers global output feedback stabilization of a class of upper-triangular nonlinear systems with multiple outputs. By coupling a finite-time convergent observer and a saturated homogeneous stabilizer, the global output feedback stabilization can be achieved without the homogeneous growth condition. The proposed techniques are also extended to more general complex nonlinear systems. Various examples, including a ball-and-beam mechanical system and a planar vertical takeoff and landing aircraft, are presented to illustrate the design.

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Barbu, C., Sepulchre, R., Lin, W., and Kokotovic, P., 1997, “Global Asymptotic Stabilization for the Ball and Beam System,” Proc. of IEEE Conf. on Decision and Control, San Diego, CA, pp. 2351–2355.
Frye, M. T., Ding, D., Qian, C., and Li, S., 2010, “Fast Convergent Observer Design for Output Feedback Stabilization of a Planar Vertical Takeoff and Landing Aircraft,” IET Control Theory Appl., 4, pp. 690–700. [CrossRef]
Liu, R., Li, S. H., and Ding, S. H., 2011, “Nested Saturation Control for Overhead Crane System,” Trans. Inst. Meas. Control (London), 34, pp. 862–875. [CrossRef]
Lin, W., and Li, X., 1999, “Synthesis of Upper-Triangular Non-Linear Systems With Marginally Unstable Free Dynamics Using State-Dependent Saturation,” Int. J. Control, 72(12), pp. 1078–1086. [CrossRef]
Teel, A. R., 1992, “Feedback Stabilization: Nonlinear Solution to Inherently Nonlinear Problems,” Ph.D. thesis, University of California, Berkeley.
Mazenc, F., and Praly, L., 1996, “Adding Integrations, Saturated Controls, and Stabilization for Feedforward Systems,” IEEE Trans. Autom. Control, 41(11), pp. 1559–1578. [CrossRef]
Sepulchre, R., Jankovic, M., and Kokotovic, P. V., 1997, “Integrator Forwarding: A New Recursive Nonlinear Robust Design,” Automatica, 33(5), pp. 979–984. [CrossRef]
Qian, C., and Li, J., 2006, “Global Output Feedback Stabilization of Upper-Triangular Nonlinear Systems Using a Homogeneous Domination Approach,” Int. J. Robust Nonlinear Control, 16(9), pp. 441–463. [CrossRef]
Lin, W., 1995, “Bounded Smooth State Feedback and a Global Separation Principle for Non-Affine Nonlinear Systems,” Syst. Control Lett., 26(1), pp. 41–53. [CrossRef]
Mazenc, F., and Vivalda, J., 2002, “Global Asymptotic Output Feedback Stabilization of Feedforward Systems,” Eur. J. Control, 8, pp. 519–530. [CrossRef]
Choi, H. L., and Tae, L. J., 2005, “Global Exponential Stabilization of a Class of Nonlinear Systems by Output Feedback,” IEEE Trans. Autom. Control, 50(2), pp. 255–257. [CrossRef]
Polendo, J., and Schrader, C., 2005, “Output Feedback Stabilization of Nonlinear Feedforward Systems Using Arbitrarily Bounded Control,” Proc. of 2005 American Control Conference, pp. 4727–4729.
Frye, M. T., Trevino, R., and Qian, C., 2007, “Output Feedback Stabilization of Nonlinear Feedforward Systems Using Low Gain Homogeneous Domination,” Proc. of 2007 IEEE International Conference on Control and Automation, pp. 422–427.
Qian, C., “A Homogeneous Domination Approach for Global Output Feedback Stabilization of a Class of Nonlinear Systems,” Proc. of 2005 American Control Conference, pp. 4708–4715.
Bhat, S. P., and Bernstein, D. S., 1998, “Continuous Finite-Time Stabilization of the Translational and Rotational Double Integrators,” IEEE Trans. Autom. Control, 43(5), pp. 678–682. [CrossRef]
Hong, Y., Huang, J., and Xu, Y., 2001, “On an Output Feedback Finite-Time Stabilization Problem,” IEEE Trans. Autom. Control, 46(2), pp. 305–309. [CrossRef]
Li, J., Qian, C., and Frye, M., “A Dual Observer Design for Global Output Feedback Stabilization of Nonlinear Systems With Low-Order and High-Order Nonlinearities,” Proc. of IEEE Conference on Decision and Control.
Ding, S., Qian, C., and Li, S., 2010, “Global Stabilization of a Class of Feedforward Systems With Lower-Order Nonlinearities,” IEEE Trans. Autom. Control, 55(3), pp. 691–696. [CrossRef]
Mazenc, F., 1997, “Stabilization of Feedforward Systems Approximated by a Non-linear Chain of Integrators,” Syst. Control Lett., 32, pp. 223–229. [CrossRef]


Grahic Jump Location
Fig. 3

Trajectories (x,vx) and their estimations (x∧,v∧x)

Grahic Jump Location
Fig. 4

Trajectories (z,vz) and their estimations (z∧,v∧z)

Grahic Jump Location
Fig. 5

Trajectories (θ,ω) and their estimations (θ∧,ω∧)

Grahic Jump Location
Fig. 1

Trajectories of x1,1 and x2,1

Grahic Jump Location
Fig. 2

Unmeasurable states and their estimates




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