Mesh stability of look-ahead interconnected systems

We define a notion of mesh stability for a class of interconnected nonlinear systems. Intuitively, mesh stability is the property of damping disturbance propagation. We derive a set of sufficient conditions to assure mesh stability of "look-ahead" interconnected systems. Mesh stability is shown to be robust with respect to structural and singular perturbations. The theory is applied to an example of formation flying.

[1]  S. Sastry.  Nonlinear Systems: Analysis, Stability, and Control , 1999 .

[2]  S. G. Deo.  On vector Lyapunov functions , 1971 .

[3]  L. Peppard,et al.  String stability of relative-motion PID vehicle control systems , 1974 .

[4]  Hassan K. Khalil,et al.  Singular perturbation methods in control : analysis and design , 1986 .

[5]  J. Hedrick,et al.  String stability of interconnected systems , 1996, IEEE Trans. Autom. Control..

[6]  R. Bellman.  Vector Lyanpunov Functions , 1962 .

[7]  D. Swaroop,et al.  String Stability Of Interconnected Systems: An Application To Platooning In Automated Highway Systems , 1997 .

[8]  Zoran Gajic,et al.  Monotonicity of algebraic Lyapunov iterations for optimal control of jump parameter linear systems , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[9]  Dragoslav D. Šiljak,et al.  Large-Scale Dynamic Systems: Stability and Structure , 1978 .

[10]  Dong Yue,et al.  An improvement on "Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty" , 2002, IEEE Trans. Autom. Control..

[11]  A. Girard,et al.  A coordinated DP control methodology for the MOB , 1999 .

[12]  J. K. Hedrick,et al.  Dynamic Coupling in Vehicles Under Automatic Control , 1994 .

[13]  Peter J Seiler,et al.  Preliminary Investigation of Mesh Stability for Linear Systems , 1999, Dynamic Systems and Control.

[14]  Miroslav Kárný,et al.  Towards fully probabilistic control design , 1996, Autom..

[15]  V. Lakshmikantham,et al.  Differential and integral inequalities : theory and applications , 1969 .

[16]  Jianhua Zhang,et al.  Bounded stochastic distributions control for pseudo-ARMAX stochastic systems , 2001, IEEE Trans. Autom. Control..