PROJECT TITLE :
Discretization for Sampled-Data Controller Synthesis via Piecewise Linear Approximation
This paper develops a replacement discretization method with piecewise linear approximation for the $L_1$ optimal controller synthesis downside of sampled-knowledge systems, that is the matter of minimizing the $L_infty$-induced norm of sampled-information systems. We apply quick-lifting on the top of the lifting technique, by that the sampling interval $[0,h)$ is split into $M$ subintervals with an equal width. The signals on each subinterval are then approximated by linear functions by introducing two varieties of 'linearizing operators’ for input and output, that leads to piecewise linear approximation of sampled-data systems. By using the arguments of preadjoint operators, we provide an important inequality that forms a theoretical basis for tackling the $L_1$ optimal controller synthesis drawback of sampled-data systems more efficiently than the traditional method. A lot of exactly, a mathematical basis for the piecewise linear approximation methodology associated with the convergence rate is shown through this inequality, and this implies that the piecewise linear approximation technique may drastically outperform the conventional technique within the $L_1$ optimal controller synthesis drawback of sampled-data systems. We have a tendency to then give a discretization procedure of sampled-information systems by that the $L_1$ optimal controller synthesis downside is converted to the discrete-time $l_1$ optimal controller synthe- is drawback. Finally, effectiveness of the proposed methodology is demonstrated through a numerical example.
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