##### Department of Mathematics,

University of California San Diego

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### Computational and Applied Mathematics Seminar

## Emre Mengi

#### UCSD

## A Backward Approach for Model Reduction

##### Abstract:

The differential equation $\dot{x}(t) = Ax(t) + Bu(t)$ coupled with the
algebraic equation $y(t) = Cx(t) + Du(t)$ where $A\in\mathbb{C}^{n\times n}$,
$B\in\mathbb{C}^{n\times m}$, $C\in\mathbb{C}^{p\times n}$ is
called a state space system and commonly employed to represent
a linear operator from an input space to an output space in control
theory. One major challenge with such a representation is that
typically $n$, the dimension of the intermediate state function $x(t)$,
is much larger than $m$ and $p$, the dimensions of the input
function $u(t)$ and the output function $y(t)$. To reduce the order of
such a system (dimension of the state space) the traditional
approaches are based on minimizing the $H_{\infty}$ norm of the
difference between the transfer functions of the original system and
the reduced-order system. We pose a backward error minimization
problem for model reduction in terms of the norms of the
perturbations to the coefficients $A$, $B$ and $C$ such that the
perturbed systems are equivalent to systems of order $r

### June 5, 2007

### 11:00 AM

### AP&M 5402

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