Model reduction for infinite dimensional systems using reciprocal transformation

In this paper we propose a model reduction for infinite dimensional systems using reciprocal transformation. The class of systems considered is that of a exponentially stable state linear systems (A;B;C), where operator A has a bounded inverse and the operator B and C are of finite-rank and bounded. We can connect the system (A;B;C) with its reciprocal system via the solutions of the Lyapunov equations. The realization of the reciprocal system is reduced by balanced truncation. This result is further translated using reciprocal transformation as the reduced-order model for the systems (A;B;C). The numerical examples are studied using simulations of Euler-Bernoulli beam to show the effectiveness of the proposed reduction method.