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We present a rigorous approach to extend balanced truncation model reduction (BTMR) to systems with inhomogeneous initial conditions, we provide an estimate for the error between the input–output maps of the original and of the reduced initial value system, and we illustrate numerically the superiority of our approach over the naive application of BTMR. When BTMR is applied to linear time invariant...
In this paper, the classical systems theoretic concepts of controllability and observability are considered for descriptor systems with an infinite-dimensional state space. These are systems of the form Exdot(t) = Ax(t) + Bu(t), y(t) = Cx(t), where x(ldr), u(ldr), and y(ldr) are functions with values in separable Hilbert spaces X, U, and Y. For the operators, we assume that E : XrarrZ, B : UrarrZ,...
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