Static output feedback stabilization: from linear to nonlinear and back

The static output feedback stabilization problem for linear and nonlinear (affine) systems is discussed. A novel necessary and sufficient condition for linear systems is proposed. For nonlinear systems a sufficient condition is established and a (partial) converse is also discussed. The nonlinear formulation is used to derive a simple characterization of stabilizing static output feedback control laws for linear systems in terms of the intersection of two convex sets and a (generically) nonconvex set. This characterization is used to establish a series of simple obstructions to the solvability of the problem for linear SISO systems. A few worked out examples complete the chapter.

[1]  B. O. Anderson,et al.  Time-varying feedback laws for decentralized control , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[2]  D. Youla,et al.  Single-loop feedback-stabilization of linear multivariable dynamical plants , 1974, Autom..

[3]  R. Skelton,et al.  Parametrization of all stabilizing controllers via quadratic Lyapunov functions , 1995 .

[4]  Chaouki T. Abdallah,et al.  Static output feedback: a survey , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[5]  G. Goodwin,et al.  Generalized sample hold functions-frequency domain analysis of robustness, sensitivity, and intersample difficulties , 1994, IEEE Trans. Autom. Control..

[6]  C. Nett,et al.  Minimal Complexity Control Law Synthesis, Part 1: Problem Formulation and Reduction to Optimal Static Output Feedback , 1989, 1989 American Control Conference.

[7]  Alessandro Astolfi,et al.  Robust output feedback stabilization of the angular velocity of a rigid body , 1999 .

[8]  A. Isidori,et al.  Asymptotic stabilization of minimum phase nonlinear systems , 1991 .

[9]  A. Isidori,et al.  Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems , 1991 .

[10]  P. Kabamba.  Control of Linear Systems Using Generalized Sampled-Data Hold Functions , 1987, 1987 American Control Conference.

[11]  Carlos E. de Souza,et al.  A necessary and sufficient condition for output feedback stabilizability , 1995, Autom..

[12]  Robert E. Skelton,et al.  Static output feedback controllers: stability and convexity , 1998, IEEE Trans. Autom. Control..

[13]  L. Ghaoui,et al.  A cone complementarity linearization algorithm for static output-feedback and related problems , 1997, IEEE Trans. Autom. Control..

[14]  Andrzej W. Olbrot,et al.  Robust stabilization of uncertain systems by periodic feedback , 1987 .

[15]  G. Gu.  Stabilizability conditions of multivariable uncertain systems via output feedback control , 1990 .

[16]  K. Wei,et al.  Stabilization of a linear plant via a stable compensator having no real unstable zeros , 1990 .

[17]  A. Isidori.  Nonlinear Control Systems , 1985 .

[18]  Dirk Aeyels,et al.  Pole assignment for linear time-invariant systems by periodic memoryless output feedback , 1992, Autom..

[19]  James Lam,et al.  Static Output Feedback Stabilization: An ILMI Approach , 1998, Autom..

[20]  Bengt Mårtensson,et al.  The order of any stabilizing regulator is sufficient a priori information for adaptive stabilization , 1985 .