Exponential stability and stabilization of nD systems

The paper considers nonlinear nD discrete and continuous systems described by a state-space model of the Roesser form where the property of exponential stability is characterized by use of a vector Lyapunov function. The property of exponential dissipativity is defined and a particular case of this property, termed exponential passivity, is used, together with a vector storage function, to develop a new method for output based control law design. An example of a system with nonlinear actuator dynamics is given to demonstrate the application effectiveness of the new results.

[1]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[2]  Krzysztof Galkowski,et al.  Stability and stabilization of systems modeled by 2D nonlinear stochastic roesser models , 2011, The 2011 International Workshop on Multidimensional (nD) Systems.

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

[4]  David J. Hill,et al.  Exponential Feedback Passivity and Stabilizability of Nonlinear Systems , 1998, Autom..

[5]  Krzysztof Galkowski,et al.  Vector Lyapunov Function based Stability of a Class of Applications Relevant 2D Nonlinear Systems , 2014 .

[6]  Krzysztof Galkowski,et al.  On the control of distributed parameter systems using a multidimensional systems setting , 2008 .

[7]  Ettore Fornasini,et al.  Doubly-indexed dynamical systems: State-space models and structural properties , 1978, Mathematical systems theory.

[8]  Krzysztof Galkowski,et al.  Control Systems Theory and Applications for Linear Repetitive Processes - Recent Progress and Open Research Questions , 2007 .

[9]  Krzysztof Galkowski,et al.  Passivity based stabilization of nonlinear 2D systems with application to iterative learning control , 2014, 2014 IEEE International Symposium on Intelligent Control (ISIC).

[10]  Panajotis Agathoklis,et al.  Stability and the Lyapunov equation for n-dimensional digital systems , 1997 .

[11]  Robert G. Landers,et al.  Iterative learning control of bead morphology in Laser Metal Deposition processes , 2013, 2013 American Control Conference.

[12]  R. Roesser.  A discrete state-space model for linear image processing , 1975 .

[13]  Emmanuel Moulay,et al.  Lyapunov Theory for 2-D Nonlinear Roesser Models: Application to Asymptotic and Exponential Stability , 2013, IEEE Transactions on Automatic Control.

[14]  Krzysztof Galkowski,et al.  Modeling and control of a sorption process using 2D systems theory , 2011, The 2011 International Workshop on Multidimensional (nD) Systems.

[15]  Jerzy E. Kurek,et al.  Stability of nonlinear time-varying digital 2-D Fornasini-Marchesini system , 2014, Multidimens. Syst. Signal Process..

[16]  Krzysztof Galkowski,et al.  Experimentally supported 2D systems based iterative learning control law design for error convergence and performance , 2010 .

[17]  S.G. Nersesov,et al.  Vector dissipativity theory for large-scale nonlinear dynamical systems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).