Abstract
The paper develops new results on stability analysis and stabilization of linear repetitive processes. Repetitive processes are a distinct subclass of two-dimensional (2D) systems, whose origins are in the modeling for control of mining and metal rolling operations. The reported systems theory for them has been applied in other areas such iterative learning control, where, uniquely among 2D systems based designs, experimental validation results have been reported. This paper uses a version of the Kalman–Yakubovich–Popov Lemma to develop new less conservative conditions for stability in terms of linear matrix inequalities, with an extension to control law design. Differential and discrete dynamics are analysed in an unified manner, and supporting numerical examples are given.
Highlights
Repetitive processes have their origins in the modeling and control of long-wall coal cutting and material rolling operations, see, e.g., Rogers et al (2007), which, in turn, cited the original work
This theory is based on a general model that includes all linear constant pass length examples as special cases. It allows specific treatment of the boundary conditions at the start of each pass, which must have a very particular and restrictive form for analysis based on the alternative above to produce correct results. Aside from their use in the analysis and control of physical examples, the repetitive process setting has been used as a basis for solving problems in other areas of control theory, such as iterative learning control (ILC) law design, see, e.g., Rogers et al (2015) and Paszke et al (2016)) and iterative algorithms for solving nonlinear dynamic optimal control problems based on the maximum principle (Roberts 2002)
This paper has developed new results on the stability and stabilization for linear repetitive processes
Summary
Repetitive processes have their origins in the modeling and control of long-wall coal cutting and material rolling operations, see, e.g., Rogers et al (2007), which, in turn, cited the original work. It allows specific treatment of the boundary conditions at the start of each pass, which must have a very particular and restrictive form for analysis based on the alternative above to produce correct results Aside from their use in the analysis and control of physical examples, the repetitive process setting has been used as a basis for solving problems in other areas of control theory, such as iterative learning control (ILC) law design, see, e.g., Rogers et al (2015) and Paszke et al (2016)) and iterative algorithms for solving nonlinear dynamic optimal control problems based on the maximum principle (Roberts 2002). Lemma 2 provides a dual version of the GKYP lemma, which is exploited in the analysis that follows
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