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Papers by Wolfgang Kliemann
Systems & Control: Foundations & Applications, 2001
ABSTRACT
[1991] Proceedings of the 30th IEEE Conference on Decision and Control, 1991
ABSTRACT
Proceedings of the 36th IEEE Conference on Decision and Control, 1997
ABSTRACT
Proceedings of 32nd IEEE Conference on Decision and Control, 1993
ABSTRACT
Systems & Control Letters, 2003
The relations between attractors, input-to-state-stability, and controllability properties are di... more The relations between attractors, input-to-state-stability, and controllability properties are discussed. In particular it is shown that loss of the attractor property under perturbations is connected with a qualitative change in the controllability properties due to a ‘merger’ with a control set.
This note proposes a topological framework for the analysis of the time shift on behaviors and it... more This note proposes a topological framework for the analysis of the time shift on behaviors and its asymptotics as time tends to in…nity. The relations to controllability properties are explored.
For L1 -families of time varying matrices centered at an unper- turbed matrix, the Lyapunov spect... more For L1 -families of time varying matrices centered at an unper- turbed matrix, the Lyapunov spectrum contains the Floquet spectrum ob- tained by considering periodically varying piecewise constant matrices. On the other hand, it is contained in the Morse spectrum of an associated flow on a vector bundle. A closer analysis of the Floquet spectrum based on geo- metric control
Systems & Control: Foundations & Applications, 2000
ABSTRACT
Lecture Notes in Mathematics, 1991
The use of Lyapunov exponents in the theory of dynamical systems or stochastic systems is often b... more The use of Lyapunov exponents in the theory of dynamical systems or stochastic systems is often based on Oseledeč's Multiplicative Ergodic Theorem. For control systems this is not possible, because each (sufficiently rich) control system contains dynamics that are not Lyapunov regular. In this paper we present an approach to study the Lyapunov spectrum of a nonlinear control system via ergodic theory of the associated control flow and its linearization. In particular, it turns out that all Lyapunov exponents are attained over so called chain control sets, and they are integrals of Lyapunov exponents on control sets with respect to flow invariant measures, whose support is contained in the lifts of control sets to UM, where U is the space of admissible control functions and M is the state space of the system. For the linearization of control systems about rest points the extremal Lyapunov exponents are analyzed, which leads to precise criteria for the stabilization and destabilization of bilinear control systems, and to robustness results for linear systems. The last section is devoted to a nonlinear example, where we combine the analysis of the global controllability structure with local linearization results and Lyapunov exponents to obtain a complete picture of control, stabilization and robustness of the system.
Control of Uncertain Systems, 1990
Systems & Control: Foundations & Applications, 2000
... The dynamics of control i Fritz Colonius, Wolfgang Kliemann. ... even if the former are not e... more ... The dynamics of control i Fritz Colonius, Wolfgang Kliemann. ... even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. ...
The relations between attractors, input-to-state-stability, and controllability prop- erties are ... more The relations between attractors, input-to-state-stability, and controllability prop- erties are discussed. In particular it is shown that loss of the attractor property under perturbations is connected with a qualitative change in the controllability properties due to a merger with a control set.
Transactions of the American Mathematical Society, 2008
This paper proposes a topological framework for the analysis of the time shift on behaviors. It i... more This paper proposes a topological framework for the analysis of the time shift on behaviors. It is shown that controllability is not a property of the time shift, while chain controllability is. This also leads to a global decomposition.
Systems & Control Letters, 1995
ABSTRACT
We investigate the stability and growth of the linear parameter-excited stochastic system xt=At x... more We investigate the stability and growth of the linear parameter-excited stochastic system xt=At xt, which At is a stationary diffusion process. The interplay between stochastic systems and associated deterministic control systems allows us to derive results on the ergodicity of (xt/|xt|, At) and so on the growth of xt. Using an effective computation procedure the 2-dimensional case is solved completely.
SIAM Journal on Applied Mathematics, 1996
ABSTRACT
Systems & Control: Foundations & Applications, 2001
ABSTRACT
[1991] Proceedings of the 30th IEEE Conference on Decision and Control, 1991
ABSTRACT
Proceedings of the 36th IEEE Conference on Decision and Control, 1997
ABSTRACT
Proceedings of 32nd IEEE Conference on Decision and Control, 1993
ABSTRACT
Systems & Control Letters, 2003
The relations between attractors, input-to-state-stability, and controllability properties are di... more The relations between attractors, input-to-state-stability, and controllability properties are discussed. In particular it is shown that loss of the attractor property under perturbations is connected with a qualitative change in the controllability properties due to a ‘merger’ with a control set.
This note proposes a topological framework for the analysis of the time shift on behaviors and it... more This note proposes a topological framework for the analysis of the time shift on behaviors and its asymptotics as time tends to in…nity. The relations to controllability properties are explored.
For L1 -families of time varying matrices centered at an unper- turbed matrix, the Lyapunov spect... more For L1 -families of time varying matrices centered at an unper- turbed matrix, the Lyapunov spectrum contains the Floquet spectrum ob- tained by considering periodically varying piecewise constant matrices. On the other hand, it is contained in the Morse spectrum of an associated flow on a vector bundle. A closer analysis of the Floquet spectrum based on geo- metric control
Systems & Control: Foundations & Applications, 2000
ABSTRACT
Lecture Notes in Mathematics, 1991
The use of Lyapunov exponents in the theory of dynamical systems or stochastic systems is often b... more The use of Lyapunov exponents in the theory of dynamical systems or stochastic systems is often based on Oseledeč's Multiplicative Ergodic Theorem. For control systems this is not possible, because each (sufficiently rich) control system contains dynamics that are not Lyapunov regular. In this paper we present an approach to study the Lyapunov spectrum of a nonlinear control system via ergodic theory of the associated control flow and its linearization. In particular, it turns out that all Lyapunov exponents are attained over so called chain control sets, and they are integrals of Lyapunov exponents on control sets with respect to flow invariant measures, whose support is contained in the lifts of control sets to UM, where U is the space of admissible control functions and M is the state space of the system. For the linearization of control systems about rest points the extremal Lyapunov exponents are analyzed, which leads to precise criteria for the stabilization and destabilization of bilinear control systems, and to robustness results for linear systems. The last section is devoted to a nonlinear example, where we combine the analysis of the global controllability structure with local linearization results and Lyapunov exponents to obtain a complete picture of control, stabilization and robustness of the system.
Control of Uncertain Systems, 1990
Systems & Control: Foundations & Applications, 2000
... The dynamics of control i Fritz Colonius, Wolfgang Kliemann. ... even if the former are not e... more ... The dynamics of control i Fritz Colonius, Wolfgang Kliemann. ... even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. ...
The relations between attractors, input-to-state-stability, and controllability prop- erties are ... more The relations between attractors, input-to-state-stability, and controllability prop- erties are discussed. In particular it is shown that loss of the attractor property under perturbations is connected with a qualitative change in the controllability properties due to a merger with a control set.
Transactions of the American Mathematical Society, 2008
This paper proposes a topological framework for the analysis of the time shift on behaviors. It i... more This paper proposes a topological framework for the analysis of the time shift on behaviors. It is shown that controllability is not a property of the time shift, while chain controllability is. This also leads to a global decomposition.
Systems & Control Letters, 1995
ABSTRACT
We investigate the stability and growth of the linear parameter-excited stochastic system xt=At x... more We investigate the stability and growth of the linear parameter-excited stochastic system xt=At xt, which At is a stationary diffusion process. The interplay between stochastic systems and associated deterministic control systems allows us to derive results on the ergodicity of (xt/|xt|, At) and so on the growth of xt. Using an effective computation procedure the 2-dimensional case is solved completely.
SIAM Journal on Applied Mathematics, 1996
ABSTRACT