D. Hinrichsen - Academia.edu (original) (raw)

Papers by D. Hinrichsen

Population reports. Series M, Special topics, 1998

Systems & Control Letters, 1993

In this note we present a method to determine and visualize the set of all complex numbers to whi... more In this note we present a method to determine and visualize the set of all complex numbers to which at least one eigenvalue of a matrix A can be shifted by real or complex perturbations of the form A ; A( ) = A + D E where D and E are xed matrices and the unknown disturbance matrix satis es k k < for a given > 0. Both real and complex perturbations are studied. The graphical method may be considered as an extension of the classical root locus method to multivariable systems and multi-parameter perturbations. The results are illustrated by various examples.

Systems & Control Letters, 2003

The relationship between various types of system transformations and pencil equivalence is studie... more The relationship between various types of system transformations and pencil equivalence is studied. A Kronecker canonical form for input pencils is described which extends Brunovsky's canonical form to arbitrary (possibly uncontrollable) generalized state space systems. Necessary conditions for a pencil to lie in the closure of a given equivalence class of pencils are stated. These conditions are shown to be sufficient for controllable input pencils of generalized state space systems

Numerische Mathematik, 1991

In this paper we investigate the set of eigenvalues of a perturbed matrix A + ∆ ∈ R n×n where A i... more In this paper we investigate the set of eigenvalues of a perturbed matrix A + ∆ ∈ R n×n where A is given and ∆ ∈ R n×n , ∆ < ρ is arbitrary. We determine a lower bound for this spectral value set which is exact for normal matrices A with well separated eigenvalues. We also investigate the behaviour of the spectral value set under similarity transformations. The results are then applied to stability radii which measure the distance of a matrix A from the set of matrices having at least one eigenvalue in a given closed instability domain C b ⊂ C.

Numerical Functional Analysis and Optimization, 1996

In this note a simple formula for the real stability radius of uncertain positive linear continuo... more In this note a simple formula for the real stability radius of uncertain positive linear continuous time systems is established and it is shown that the real stability radius coincides with the complex one. Arbitrary disturbance norms induced by monotonic vector norms (e.g. p-norms, 1 p 1) are considered. The distance of intervals of positive systems from instability is also determined.

Mathematics of Control, Signals, and Systems, 1997

In this paper, we study the high gain feedback classi cation problem for generalized state space ... more In this paper, we study the high gain feedback classi cation problem for generalized state space systems. We solve this problem for proportional and derivative feedback transformations of regularizable systems, i.e. we give necessary and su cient conditions for a regularizable system to be a limit of a given system under high gain proportional and derivative feedback. We also derive a new complete set of invariants for proportional feedback equivalence and specify a set of necessary conditions for a system to be limit of another system under these feedback transformations. The necessary conditions are su cient for arbitrary state space systems and for controllable singular systems.

International Journal of Robust and Nonlinear Control, 1999

In this paper we consider discrete-time, linear stochastic systems with random state and input ma... more In this paper we consider discrete-time, linear stochastic systems with random state and input matrices which are subject to stochastic disturbances and controlled by dynamic output feedback. The aim is to develop an H 1 -type theory for such systems. For this class of systems a Stochastic Bounded Real Lemma is derived which provides the basis for a Linear Matrix Inequality (LMI) approach similar to but more general than the one presented in 14] for stochastic di erential systems. Necessary and su cient conditions are derived for the existence of a stabilizing controller which reduces the norm of the closed loop perturbation operator to a level below a given threshold . These conditions take the form of coupled nonlinear matrix inequalities. In the absence of the stochastic terms they reduce to the linear matrix inequalities of deterministic H 1 -theory for discrete time systems.

Automatica, 2000

We consider stochastic discrete-time systems with multiplicative noise which are controlled by dy... more We consider stochastic discrete-time systems with multiplicative noise which are controlled by dynamic output feedback and subjected to blockdiagonal stochastic parameter perturbations. Stability radii for these systems are characterized via scaling techniques and it is shown that for real data, the real and the complex stability radii coincide. In a second part of the paper we investigate the problem of maximizing the stability radii by dynamic output feedback. Necessary and su cient conditions are derived for the existence of a stabilizing compensator which ensures that the stability radius is above a prespeci ed level. These conditions consist of parametrized matrix inequalities and a coupling condition.

SIAM Journal on Control and Optimization, 1978

This paper presents a unified approach to diverse optimal control problems for hereditary differe... more This paper presents a unified approach to diverse optimal control problems for hereditary differential systems (HDS). An abstract local maximum principle is established via the Dubovitskii-Milyutin method. It yields necessary conditions for the optimal control of HDS towards surfaces in R" and towards target sets in function spaces. Nondegeneracy criteria are included. It is shown that the necessary conditions are sufficient in the case of linear HDS with convex cost functionals. Analogous results are obtained for systems described by Fredholm equations with general control action. For Fredholm systems with targets in function spaces, the attainability space is investigated, criteria for to be closed are established and full attainability is characterized.