Stability and Stabilization of Differential Nonlinear Repetitive Processes with Applications

Abstract Repetitive processes are a class of two-dimensional systems that arise in the modeling of physical examples and also the control systems theory developed for them has, in the case of linear dynamics, been applied to design iterative learning control laws with experimental verification. This paper gives new results on the stability of nonlinear differential repetitive processes for applications where a linearized model is either very limited or not applicable. The stability results are then applied to the design of iterative learning control laws in the presence of uncertain parameters and to the same problem when random failures occur that are modeled by a homogeneous Markov chain with a finite set of states. In both cases the computations required are expressed as a finite set of linear matrix inequalities.

[1]  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.

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

[3]  R. P. Marques,et al.  Discrete-Time Markov Jump Linear Systems , 2004, IEEE Transactions on Automatic Control.

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

[5]  Krzysztof Galkowski,et al.  Iterative learning control under parameter uncertainty and failures , 2012, 2012 IEEE International Symposium on Intelligent Control.

[6]  Huijun Gao,et al.  Stabilization and H∞ control of two-dimensional Markovian jump systems , 2004, IMA J. Math. Control. Inf..

[7]  M. Mariton,et al.  Jump Linear Systems in Automatic Control , 1992 .

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

[9]  E. Rogers,et al.  Linear-quadratic parametrization of stabilizing controls in discrete-time 2D systems , 2011 .

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

[11]  Huijun Gao,et al.  I filtering for 2D Markovian jump systems , 2008, Autom..

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

[13]  Kiev,et al.  Stability and Stabilization of Nonlinear Systems with Random Structure , 2002 .

[14]  A A Martynyuk,et al.  Stability and Stabilization of Nonlinear Systems with Random Structures , 2002 .

[15]  T.-P. Azevedo-Perdicoúlis,et al.  Disturbance attenuation of linear quadratic OL-Nash games on repetitive processes with smoothing on the gas dynamics , 2012, Multidimens. Syst. Signal Process..