21 citations · 85 across the 17 of their papers we have counts for
23 papers
Global controllability properties of linear control systems
Fritz Colonius, Alexandre J. Santana
For linear control systems with bounded control range, the state space is compactified using the Poincaré sphere. The linearization of the induced control flow allows the construct…
Nonautonomous control systems and skew product flows
Fritz Colonius, Roberta Fabbri
For nonautonomous control systems with compact control range, associated control flows are introduced. This leads to several skew product flows with various base spaces. The contro…
Control semiflows, chain controllability, and the Selgrade decomposition for linear delay systems
Fritz Colonius
A continuous semiflow is introduced for linear control systems with delays in the states and controls and bounded control range. The state includes the control functions. It is pro…
Strong chain control sets and affine control systems
Fritz Colonius, Alexandre J. Santana
For control-affine systems on non-compact manifolds, the notion of strong chain control sets is introduced and related to the strong chain transitivity of the associated control fl…
Chain controllability of linear control systems
Fritz Colonius, Alexandre J. Santana, Eduardo C. Viscovini
For linear control systems with bounded control range, chain controllability properties are analyzed. It is shown that there exists a unique chain control set and that it equals th…
Chain recurrence and Selgrade`s theorem for affine flows
Fritz Colonius, Alexandre J. Santana
Affine flows on vector bundles with chain transitive base flow are lifted to linear flows and the decomposition into exponentially separated subbundles provided by Selgrade's theor…
Controllability of periodic linear systems, the Poincare sphere, and quasi-affine systems
Fritz Colonius, Alexandre Santana, Juliana Setti
For periodic linear control systems with bounded control range, an autonomized system is introduced by adding the phase to the state of the system. Here a unique control set (i.e.,…
On the global behavior of linear flows
Fritz Colonius
For linear flows on vector bundles, it is analyzed when subbundles in the Selgrade decomposition yield chain transitive subsets for the induced flow on the associated Poincaré sphe…
Control Sets for Affine Systems, Spectral Properties and Projective Spaces
Fritz Colonius, Alexandre J. Santana, Juliana Setti
For affine control systems with bounded control range the control sets, i.e., the maximal subsets of complete approximate controllability, are studied using spectral properties. Fo…
Control Sets for Bilinear and Affine Systems
Fritz Colonius, Juliana Raupp, Alexandre J. Santana
For homogeneous bilinear control systems, the control sets are characterized using a Lie algebra rank condition for the induced systems on projective space. This is based on a clas…
Controllability near a homoclinic bifurcation
Fritz Colonius, Amani Hasan, Gholam Reza Rokni Lamouki
Controllability properties are studied for control-affine systems depending on a parameter and with constrained control values. The uncontrolled systems in dimension two and three…
Entropy for practical stabilization
Fritz Colonius, Boumediene Hamzi
For deterministic continuous time nonlinear control systems, epsilon-practical stabilization entropy and practical stabilization entropy are introduced. Here the rate of attraction…
Outer invariance entropy for discrete-time linear systems on Lie groups
Fritz Colonius, João A. N. Cossich, Alexandre J. Santana
We introduce discrete-time linear control systems on connected Lie groups and present an upper bound for the outer invariance entropy of admissible pairs (K,Q). If the stable subgr…
Quasi-ergodic limits for finite absorbing Markov chains
Fritz Colonius, Martin Rasmussen
We present formulas for quasi-ergodic limits of finite absorbing Markov chains. Since the irreducible case has been solved in 1965 by Darroch and Seneta, we focus on the reducible…
Controllability properties and invariance pressure for linear discrete-time systems
Fritz Colonius, João A. N. Cossich, Alexandre J. Santana
For linear control systems in discrete time controllability properties are characterized. In particular, a unique control set with nonvoid interior exists and it is bounded in the…
Bounds for Invariance Pressure
Fritz Colonius, Alexandre J. Santana, João A. N. Cossich
This paper provides an upper for the invariance pressure of control sets with nonempty interior and a lower bound for sets with finite volume. In the special case of the control se…
Invariance pressure of control sets
Fritz Colonius, João A. N. Cossich, Alexandre J. Santana
The invariance pressure of continuous-time control systems with initial states in a set K which are to be kept in a set Q is introduced and a number of results are derived, mainly…
Invariance Pressure for Control Systems
Fritz Colonius, Alexandre J. Santana, João A. N. Cossich
Notions of invariance pressure for control systems are introduced based on weights for the control values. The equivalence is shown between inner invariance pressure based on spann…
Invariance entropy, quasi-stationary measures and control sets
Fritz Colonius
For control systems in discrete time, this paper discusses measure-theoretic invariance entropy for a subset Q of the state space with respect to a quasi-stationary measure obtaine…
Supports of Invariant Measures for Piecewise Deterministic Markov Processes
Michel Benaïm, Fritz Colonius, Lettau Ralph
For a class of piecewise deterministic Markov processes, the supports of the invariant measures are characterized. This is based on the analysis of controllability properties of an…
Decay rates for stabilization of linear continuous-time systems with random switching
Fritz Colonius, Guilherme Mazanti
For a class of linear switched systems in continuous time a controllability condition implies that state feedbacks allow to achieve almost sure stabilization with arbitrary exponen…
Kernel Methods for Linear Discrete-Time Equations
Fritz Colonius, Boumediene Hamzi
Methods from learning theory are used in the state space of linear dynamical and control systems in order to estimate the system matrices. An application to stabilization via algeb…
Growth rates for persistently excited linear systems
Yacine Chitour, Fritz Colonius, Mario Sigalotti
We consider a family of linear control systems where belongs to a given class of persistently exciting signals. We seek maximal -uniform stabilisation and d…