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Interview with Mark Cooke
Mark Cooke
Jan 01, 0001
In his March 25, 2015 interview with Jenna Kasmarik, Mark Cooke details the role Title IX has played in athletics at Winthrop. Cooke details changes in recruitment and facilities. He also shares why he's stayed at Winthrop for...
Published by: Winthrop University
Model order reduction by balanced proper orthogonal decomposition and by rational interpolation
Mark R Opmeer
Feb 01, 2012
We show that model order reduction by rational interpolation (also known as moment matching or rational Krylov) can be seen as the special case of balanced Proper Orthogonal Decomposition where all the snapshots are retained and...
Decay of Hankel singular values of analytic control systems
Mark R Opmeer
Oct 01, 2010
We show that control systems with an analytic semigroup and control and observation operators that are not too unbounded have a Hankel operator that belongs to the Schatten class S-p for all positive p. This implies that the...
Model order reduction by balanced proper orthogonal decomposition and by rational interpolation
Mark R Opmeer
Feb 01, 2012
We show that model order reduction by rational interpolation (also known as moment matching or rational Krylov) can be seen as the special case of balanced Proper Orthogonal Decomposition where all the snapshots are retained and...
Decay of Hankel singular values of analytic control systems
Mark R Opmeer
Oct 01, 2010
We show that control systems with an analytic semigroup and control and observation operators that are not too unbounded have a Hankel operator that belongs to the Schatten class S-p for all positive p. This implies that the...
Coprime factorization and robust stabilization for discrete-time infinite-dimensional systems
We solve the problem of robust stabilization with respect to right-coprime factor perturbations for irrational discrete-time transfer functions. The key condition is that the associated dynamical system and its dual should...
A counterexample to "positive realness preserving model reduction with H-infinity norm error bounds"
We provide a counterexample to the H-infinity error bound for the difference of a positive real transfer function and its positive real balanced truncation stated in "Positive realness preserving model reduction with H-infinity...
Non-dissipative boundary feedback for Rayleigh and Timoshenko beams
We show that a non-dissipative feedback that has been shown in the literature to exponentially stabilize an EulerBernoulli beam makes a Rayleigh beam and a Timoshenko beam unstable.
Bounded real and positive real balanced truncation for infinite-dimensional systems
Bounded real balanced truncation for infinite-dimensional systems is considered. This provides reduced order finite-dimensional systems that retain bounded realness. We obtain an error bound analogous to the finite-dimensional...
Coprime factorization and optimal control on the doubly infinite discrete time axis
We study the problem of strongly coprime factorization over H-infinity of the unit disc. We give a necessary and sufficient condition for the existence of such a coprime factorization in terms of an optimal control problem over...
Bounded real and positive real balanced truncation for infinite-dimensional systems
Bounded real balanced truncation for infinite-dimensional systems is considered. This provides reduced order finite-dimensional systems that retain bounded realness. We obtain an error bound analogous to the finite-dimensional...
Finite-rank ADI iteration for operator Lyapunov equations
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...
Optimal input-output stabilization of infinite-dimensional discrete time-invariant linear systems by output injection
We study the optimal input-output stabilization of discrete time-invariant linear systems in Hilbert spaces by output injection. We show that a necessary and sufficient condition for this problem to be solvable is that the...
Coprime factorization and robust stabilization for discrete-time infinite-dimensional systems
We solve the problem of robust stabilization with respect to right-coprime factor perturbations for irrational discrete-time transfer functions. The key condition is that the associated dynamical system and its dual should...
A counterexample to "positive realness preserving model reduction with H-infinity norm error bounds"
We provide a counterexample to the H-infinity error bound for the difference of a positive real transfer function and its positive real balanced truncation stated in "Positive realness preserving model reduction with H-infinity...
Optimal State Feedback Input-Output Stabilization of Infinite-Dimensional Discrete Time-Invariant Linear Systems
We study the optimal input-output stabilization of discrete time-invariant linear systems in Hilbert spaces by state feedback. We show that a necessary and sufficient condition for this problem to be solvable is that the...
Optimal State Feedback Input-Output Stabilization of Infinite-Dimensional Discrete Time-Invariant Linear Systems
We study the optimal input-output stabilization of discrete time-invariant linear systems in Hilbert spaces by state feedback. We show that a necessary and sufficient condition for this problem to be solvable is that the...
State space formulas for a solution of the suboptimal Nehari problem on the unit disc
We give state space formulas for a ("central") solution of the suboptimal Nehari problem for functions defined on the unit disc and taking values in the space of bounded operators in separable Hilbert spaces. Instead of assuming...
State space formulas for a solution of the suboptimal Nehari problem on the unit disc
We give state space formulas for a ("central") solution of the suboptimal Nehari problem for functions defined on the unit disc and taking values in the space of bounded operators in separable Hilbert spaces. Instead of assuming...
Infinite-dimensional negative imaginary systems
Mark Opmeer
Dec 01, 2011
We consider second order infinite-dimensional systems with force control and collocated position measurement interconnected with finite-dimensional controllers of the same type. We show that under assumptions that generalize...
The state space isomorphism theorem for discrete-time infinite-dimensional systems
It is well-known that the state space isomorphism theorem fails in infinite-dimensional Hilbert spaces: there exist minimal discrete-time systems (with Hilbert space state spaces) which have the same impulse response, but which...
Coprime factorization and optimal control on the doubly infinite discrete time axis
We study the problem of strongly coprime factorization over H-infinity of the unit disc. We give a necessary and sufficient condition for the existence of such a coprime factorization in terms of an optimal control problem over...
Optimal input-output stabilization of infinite-dimensional discrete time-invariant linear systems by output injection
We study the optimal input-output stabilization of discrete time-invariant linear systems in Hilbert spaces by output injection. We show that a necessary and sufficient condition for this problem to be solvable is that the...
Non-dissipative boundary feedback for Rayleigh and Timoshenko beams
We show that a non-dissipative feedback that has been shown in the literature to exponentially stabilize an EulerBernoulli beam makes a Rayleigh beam and a Timoshenko beam unstable.
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