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- Timo Reis, Tatjana Stykel
- IEEE Transactions on Computer-Aided Design of…
- 2010

We present a passivity-preserving balanced truncation model reduction method for differential-algebraic equations arising in circuit simulation. This method is based on balancing the solutions of projected Lur'e equations. By making use of the special structure of circuit equations, we can reduce the numerical effort for balanced truncation significantly.… (More)

- Thomas Berger, Timo Reis
- 2012

Different concepts related to controllability of differential-algebraic equations are described. The class of systems considered consists of linear differential-algebraic equations with constant coefficients. Regularity, which is, loosely speaking, a concept related to existence and uniqueness of solutions for any inhomogeneity, is not required in this… (More)

- Timo Reis, Tatjana Stykel
- Int. J. Control
- 2010

- Matthias Heinkenschloss, Timo Reis, Athanasios C. Antoulas
- Automatica
- 2011

- Mark R. Opmeer, Timo Reis, W. Wollner
- SIAM J. Control and Optimization
- 2013

We give an algorithmic approach to the approximative solution of operator Lyapunov equations for controllability. Motivated by the successfully applied alternating direction implicit (ADI) iteration for matrix Lyapunov equations, we consider this method for the determination of Gramian operators of infinite-dimensional control systems. In the case where the… (More)

- Philip Losse, Volker Mehrmann, Lisa Katrin Poppe, Timo Reis
- SIAM J. Control and Optimization
- 2008

- Timo Reis, Tatjana Stykel
- SIAM J. Applied Dynamical Systems
- 2011

We apply Lyapunov-based balanced truncation model reduction method to differential-algebraic equations arising in modeling of RC circuits. This method is based on diagonalizing the solution of one projected Lyapunov equation. It is shown that this method preserves passivity and delivers an error bound. By making use of the special structure of circuit… (More)

- Philip Losse, Timo Reis
- 2008

The H∞ control problem is studied for linear constant coefficient descriptor systems. Necessary and sufficient optimality conditions are derived for systems of arbitrary index. These conditions are formulated in terms of deflating subspaces of even matrix pencils containing only the parameters of the original system. It is shown that this approach leads to… (More)

- Timo Reis, Elena Virnik
- SIAM J. Control and Optimization
- 2009

We propose a model reduction method for positive systems that ensures the positivity of the reduced-order model. In the standard as well as in the descriptor case, for continuous-time and discrete-time systems, our approach is based on constructing diagonal solutions of Lyapunov inequalities. These are linear matrix inequalities (LMIs), which are shown to… (More)

- Thomas Berger, Achim Ilchmann, Timo Reis
- MCSS
- 2012

We study the class of linear differential-algebraic m-input m-output systems which have a transfer function with proper inverse. A sufficient condition for the transfer function to have proper inverse it that the system has ‘strict and non-positive relative degree’. We present two main results: First, a so called ‘zero dynamics form’ is derived: this form… (More)