Global sampled-data output feedback stabilization for a class of uncertain nonlinear systems

This paper investigates the global asymptotical stabilization using sampled-data output feedback (i.e., not all state information is available at the output) for a class of nonlinear systems which have uncontrollable and unobservable linearizations around the origin. A homogeneous version of Gronwall–Bellman inequality is introduced as the essential tool to estimate trajectory of nonlinear sampled-data control systems between two successive sampling instants. With the help of this new tool as well as the homogeneous domination approach, a sampled-data observer-based controller is constructed to globally asymptotically stabilize the origin of the nonlinear system under a homogeneous growth condition.

[1]  P. Kokotovic,et al.  Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations , 1999 .

[2]  Yiguang Hong,et al.  Adaptive finite-time control of nonlinear systems with parametric uncertainty , 2006, IEEE Transactions on Automatic Control.

[3]  C. Qian,et al.  A generalized homogeneous domination approach for global stabilization of inherently nonlinear systems via output feedback , 2007 .

[4]  C. Kravaris,et al.  Global stability results for systems under sampled-data control , 2006, 2007 European Control Conference (ECC).

[5]  Zhong-Ping Jiang,et al.  Small-gain theorem for a wide class of feedback systems with control applications , 2007, 2007 European Control Conference (ECC).

[6]  M. Kawski.  Stabilization of nonlinear systems in the plane , 1989 .

[7]  Ji Li,et al.  A dual‐observer design for global output feedback stabilization of nonlinear systems with low‐order and high‐order nonlinearities , 2009 .

[8]  W. Dayawansa,et al.  Global stabilization by output feedback: examples and counterexamples , 1994 .

[9]  Nicolas Marchand,et al.  A General Formula for Event-Based Stabilization of Nonlinear Systems , 2013, IEEE Transactions on Automatic Control.

[10]  Xinghuo Yu,et al.  Chattering-free discrete-time sliding mode control , 2016, Autom..

[11]  Wei Lin,et al.  Recursive Observer Design, Homogeneous Approximation, and Nonsmooth Output Feedback Stabilization of Nonlinear Systems , 2006, IEEE Transactions on Automatic Control.

[12]  Dragan Nesic,et al.  Explicit Computation of the Sampling Period in Emulation of Controllers for Nonlinear Sampled-Data Systems , 2009, IEEE Transactions on Automatic Control.

[13]  Cong-Ran Zhao,et al.  Global stabilization of stochastic high-order feedforward nonlinear systems with time-varying delay , 2014, Autom..

[14]  Chunjiang Qian,et al.  Global Output Feedback Stabilization of a Class of Nonlinear Systems via Linear Sampled-Data Control , 2012, IEEE Transactions on Automatic Control.

[15]  Yu. S. Ledyaev,et al.  Asymptotic controllability implies feedback stabilization , 1997, IEEE Trans. Autom. Control..

[16]  Shihua Li,et al.  Semi‐global stabilization via linear sampled‐data output feedback for a class of uncertain nonlinear systems , 2015 .

[17]  Liang Liu,et al.  Output-feedback stabilization for stochastic high-order nonlinear systems with time-varying delay , 2011, Autom..

[18]  Lars Grüne,et al.  Homogeneous State Feedback Stabilization of Homogenous Systems , 2000, SIAM J. Control. Optim..

[19]  Patrick Coirault,et al.  Stability of homogeneous nonlinear systems with sampled-data inputs , 2017, Autom..

[20]  Wei Lin,et al.  On p-normal forms of nonlinear systems , 2003, IEEE Trans. Autom. Control..

[21]  Hassan K. Khalil,et al.  Multirate Sampled-Data Output Feedback Control With Application to Smart Material Actuated Systems , 2009, IEEE Transactions on Automatic Control.

[22]  C. De Persis,et al.  On stabilization of nonlinear systems under data rate constraints using output measurements , 2006 .

[23]  Wei Lin,et al.  A continuous feedback approach to global strong stabilization of nonlinear systems , 2001, IEEE Trans. Autom. Control..

[24]  Hassan K. Khalil,et al.  Output feedback sampled-data control of nonlinear systems using high-gain observers , 2001, IEEE Trans. Autom. Control..

[25]  Karl Johan Åström,et al.  Computer-Controlled Systems: Theory and Design , 1984 .

[26]  David H. Owens,et al.  Fast Sampling and Stability of Nonlinear Sampled-Data Systems: Part 1. Existence Theorems , 1990 .

[27]  Shihua Li,et al.  Global Stabilization via Sampled-Data Output Feedback for a Class of Linearly Uncontrollable and Unobservable Systems , 2016, IEEE Transactions on Automatic Control.

[28]  Gang Feng,et al.  Cooperative control of multiple stochastic high-order nonlinear systems , 2017, Autom..

[29]  Guanghui Wen,et al.  Discrete-Time Fast Terminal Sliding Mode Control for Permanent Magnet Linear Motor , 2018, IEEE Transactions on Industrial Electronics.