Vector Lyapunov function approach to measurement feedback stabilization of large-scale nonlinear systems

The paper considers the problem of measurement feedback decentralized stabilization of large-scale interconnected nonlinear systems. Motivated by the recent developments on control vector Lyapunov functions, the notion of an output control vector Lyapunov function is defined which serves as a starting point for the investigation of a decentralized version of feedback stabilization problem for such systems. This paper focuses on the measurement feedback decentralized stabilization problem. The main contributions of this paper are solutions to the static version of the problem. An example is given to illustrate the proposed design methods.

[1]  R. Freeman,et al.  Robust Nonlinear Control Design: State-Space and Lyapunov Techniques , 1996 .

[2]  V. Matrosov On the theory of stability of motion , 1962 .

[3]  V. Lakshmikantham,et al.  Vector Lyapunov Functions and Stability Analysis of Nonlinear Systems , 1991 .

[4]  J. Neuberger Qualitative analysis of large scale dynamical systems , 2007 .

[5]  Sergey V. Drakunov,et al.  Stabilization and tracking control for an extended Heisenberg system with a drift , 2005, Syst. Control. Lett..

[6]  Björn Rüffer,et al.  Connection between cooperative positive systems and integral input-to-state stability of large-scale systems , 2010, Autom..

[7]  Eduardo Sontag A universal construction of Artstein's theorem on nonlinear stabilization , 1989 .

[8]  Z. Artstein Stabilization with relaxed controls , 1983 .

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

[10]  Wassim M. Haddad,et al.  On the stability and control of nonlinear dynamical systems via vector Lyapunov functions , 2006, IEEE Transactions on Automatic Control.

[11]  J. Tsinias,et al.  Output feedback stabilization , 1990 .

[12]  W. Haddad,et al.  Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach , 2008 .

[13]  Valery Ugrinovskii,et al.  Distributed H ∞ consensus-based estimation of uncertain systems via dissipativity theory , 2011 .

[14]  B. Dundas,et al.  DIFFERENTIAL TOPOLOGY , 2002 .

[15]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[16]  J. Tsinias Optimal controllers and output feedback stabilization , 1990 .

[17]  Iasson Karafyllis,et al.  A Vector Lyapunov Function Characterization of Input-to-State Stability with Application to Robust Global Stabilization of the Chemostat , 2008, Eur. J. Control.

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

[19]  Valery A. Ugrinovskii,et al.  Distributed robust filtering with Hinfinity consensus of estimates , 2011, Autom..

[20]  Dragoslav D. Šiljak,et al.  Decentralized control of complex systems , 2012 .