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A new approach to strong practical stability and stabilization of discrete linear repetitive processes
No full textThe 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2010), Budapest, Hungary, 5-9 July 2010
Strong practical stability and control of uncertain discrete linear repetitive processes
No full textStrong practical stability and stabilization of discrete linear repetitive processes
No full textThis paper considers two-dimensional (2D) discrete linear systems recursive over the upper right quadrant described by well known state-space models. Included are discrete linear repetitive processes that evolve over subset of this quadrant. A stability theory exists for these processes based on a bounded-input bounded-output approach and there has also been work on the design of stabilizing control laws, elements of which have led to the assertion that this stability theory is too strong in many cases of applications interest. This paper develops so-called strong practical stability as an alternative in such cases. The analysis includes computationally efficient tests that lead directly to the design of stabilizing control laws, including the case when there is uncertainty associated with the process model. The results are illustrated by application to a linear model approximation of the dynamics of a metal rolling process
New results on strong practical stability and stabilization of discrete linear repetitive processes
No full textDiscrete linear repetitive processes operate over a subset of the upper-right quadrant of the 2D plane. Theyarise in the modeling of physical processes and also the existing systems theory for them can be used toeffect in solving control problems for other classes of systems, including iterative learning control design.This paper uses a form of the generalized Kalman–Yakubovich–Popov (GKYP) Lemma to develop newlinear matrix inequality (LMI) based stability conditions and control law design algorithms for the strongpractical stability property. Relative to alternatives, the LMIs for stability have a simpler structure andit is not required to impose particular structures on the matrix variables. These properties are extendedto control law design, including those where state vector access is not required. Illustrative numericalsimulation examples conclude the paper
A Simplified Approach to Iterative Learning Control Based on Strong Practical Stability of Repetitive Processes
No full textStability and Stabilization of a Class of Ill-conditioned Second Order Differential Linear Repetitive
No full textLMI based Stability and Stabilization of Second-order Linear Repetitive Processes
No full textThis paper develops new results on the stability and control of a class of linear repetitive processes described by a second-order matrix discrete or differential equation. These are developed by transformation of the secondorder dynamics to those of an equivalent first-order descriptor state-space model, thus avoiding the need to invert a possibly ill-conditioned leading coefficient matrix in the original model
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