2019/04/22 by Sachin Shivakumar, Shivakumar, Sachin, Amritam Das +4 · 1 citation
Mathematics · Engineering · Computer Science · #Numerical methods for differential equations #Electromagnetic Simulation and Numerical Methods #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.1904.10091
In this paper, we consider input-output properties of linear systems\nconsisting of PDEs on a finite domain coupled with ODEs through the boundary\nconditions of the PDE. This framework can be used to represent e.g. a lumped\nmass fixed to a beam or a system with delay. This work generalizes the\nsufficiency proof of the KYP Lemma for ODEs to coupled ODE-PDE systems using a\nrecently developed concept of fundamental state and the associated\nboundary-condition-free representation. The conditions of the generalized KYP\nare tested using the PQRS positive matrix parameterization of operators\nresulting in a finite-dimensional LMI, feasibility of which implies prima facie\nprovable passivity or L2-gain of the system. No discretization or approximation\nis involved at any step and we use numerical examples to demonstrate that the\nbounds obtained are not conservative in any significant sense and that\ncomputational complexity is lower than existing methods involving\nfinite-dimensional projection of PDEs.\n