XW Control of Nonlinear Systems : A Convex Characterization

In this note we study the stability properties of linear time-invariant delay systems. The specific notion under consideration is asymptotic stability independent of delay. As an attempt to achieve a compromise between the complexity and tightness of various stability tests, we present a number of sufficient stability conditions which improve several previously available sufficient conditions and which are also much easier to verify than the known necessary and sufficient conditions.

[1]  P. S. Bauer Dissipative Dynamical Systems: I. , 1931, Proceedings of the National Academy of Sciences of the United States of America.

[2]  Melvyn Stuart Berger,et al.  Perspectives in nonlinearity : an introduction to nonlinear analysis , 1968 .

[3]  D. Lukes Optimal Regulation of Nonlinear Dynamical Systems , 1969 .

[4]  W. Kahan,et al.  NORM-PRESERVING DILATIONS AND THEIR APPLICATIONS TO OPTIMAL ERROR BOUNDS* , 1982 .

[5]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[6]  P. Khargonekar,et al.  State-space solutions to standard H2 and H∞ control problems , 1988, 1988 American Control Conference.

[7]  Alberto Isidori,et al.  Nonlinear control systems: an introduction (2nd ed.) , 1989 .

[8]  A. Packard,et al.  A collection of robust control problems leading to LMIs , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[9]  Tryphon T. Georgiou,et al.  The parallel projection operators of a nonlinear feedback system , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[10]  R. Skelton,et al.  A complete solution to the general H∞ control problem: LMI existence conditions and state space formulas , 1993, 1993 American Control Conference.

[11]  J. Doyle,et al.  H∞ Control of Nonlinear Systems: A Class of Controllers , 1993 .

[12]  G. Balas,et al.  Control of Parameter-Dependent Systems: Applications to H/sub /spl infin/ Gain-Scheduling , 1993, Proceedings. The First IEEE Regional Conference on Aerospace Control Systems,.

[13]  Andrew Packard,et al.  The complex structured singular value , 1993, Autom..

[14]  J. William Helton,et al.  An inequality governing nonlinear H ∞ control , 1994 .

[15]  Wei-Min Lu,et al.  Robustness analysis and synthesis for nonlinear uncertain systems , 1997, IEEE Trans. Autom. Control..