Coprime Factor Reduction of H-infinity Controllers

We consider the efficient solution of the coprime factorization based H infinity controller approximation problems by using frequency-weighted balancing related model reduction approaches. It is shown that for a class of frequency-weighted performance preserving coprime factor reduction as well as for a relative error coprime factor reduction method, the computation of the frequency-weighted controllability and observability grammians can be done by solving Lyapunov equations of the order of the controller. The new approach can be used in conjunction with accuracy enhancing square-root and balancing-free techniques developed for the balancing related coprime factors based model reduction

Computation of transfer function matrices of periodic systems

We present a numerical approach to evaluate the transfer function matrices of a periodic system corresponding to lifted state-space representations as constant systems. The proposed pole-zero method determines each entry of the transfer function matrix in a minimal zeros-poles- gain representation. A basic computational ingredient for this method is the extended periodic real Schur form of a periodic matrix, which underlies the computation of minimal realizations and system poles. To compute zeros and gains, fast algorithms are proposed, which are specially tailored to particular single-input single-output periodic systems. The new method relies exclusively on reliable numerical computations and is well suited for robust software implementations

Identification and data-driven model reduction of state-space representations of lossless and dissipative systems from noise-free data

We illustrate procedures to identify a state-space representation of a lossless- or dissipative system from a given noise-free trajectory; important special cases are passive- and bounded-real systems. Computing a rank-revealing factorization of a Gramian-like matrix constructed from the data, a state sequence can be obtained; state-space equations are then computed solving a system of linear equations. This idea is also applied to perform model reduction by obtaining a balanced realization directly from data and truncating it to obtain a reduced-order mode

Balanced truncation for linear switched systems

In this paper, we present a theoretical analysis of the model reduction algorithm for linear switched systems. This algorithm is a reminiscence of the balanced truncation method for linear parameter varying systems. Specifically in this paper, we provide a bound on the approximation error in L2 norm for continuous-time and l2 norm for discrete-time linear switched systems. We provide a system theoretic interpretation of grammians and their singular values. Furthermore, we show that the performance of bal- anced truncation depends only on the input-output map and not on the choice of the state-space representation. For a class of stable discrete-time linear switched systems (so called strongly stable systems), we define nice controllability and nice observability grammians, which are genuinely related to reachability and controllability of switched systems. In addition, we show that quadratic stability and LMI estimates of the L2 and l2 gains depend only on the input-output map.Comment: We have corrected a number of typos and inconsistencies. In addition, we added new results in Theorem

Perfect initialization of a quantum computer of neutral atoms in an optical lattice of large lattice constant

We propose a scheme for the initialization of a quantum computer based on neutral atoms trapped in an optical lattice with large lattice constant. Our focus is the development of a compacting scheme to prepare a perfect optical lattice of simple orthorhombic structure with unit occupancy. Compacting is accomplished by sequential application of two types of operations: a flip operator that changes the internal state of the atoms, and a shift operator that moves them along the lattice principal axis. We propose physical mechanisms for realization of these operations and we study the effects of motional heating of the atoms. We carry out an analysis of the complexity of the compacting scheme and show that it scales linearly with the number of lattice sites per row of the lattice, thus showing good scaling behavior with the size of the quantum computer.Comment: 18 page

Finding weakly reversible realizations of chemical reaction networks using optimization

An algorithm is given in this paper for the computation of dynamically equivalent weakly reversible realizations with the maximal number of reactions, for chemical reaction networks (CRNs) with mass action kinetics. The original problem statement can be traced back at least 30 years ago. The algorithm uses standard linear and mixed integer linear programming, and it is based on elementary graph theory and important former results on the dense realizations of CRNs. The proposed method is also capable of determining if no dynamically equivalent weakly reversible structure exists for a given reaction network with a previously fixed complex set.Comment: 18 pages, 9 figure