Let H denote the 3-dimensional Heisenberg Lie group. The main purpose of this paper is to classify all possible linear control systems on the homogeneous spaces of H through its closed subgroups. We expose a detailed ...
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Let H denote the 3-dimensional Heisenberg Lie group. The main purpose of this paper is to classify all possible linear control systems on the homogeneous spaces of H through its closed subgroups. We expose a detailed study on the control behavior (i.e., controllability property and control sets) of some particular dynamics evolving on non simply connected homogeneous (state) spaces of dimension two and three.
In this paper, we show that for a linearcontrol system on a nilpotent Lie group, the Lie algebra rank condition is enough to assure the existence of a control set with a nonempty interior, as soon as one impose a com...
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In this paper, we show that for a linearcontrol system on a nilpotent Lie group, the Lie algebra rank condition is enough to assure the existence of a control set with a nonempty interior, as soon as one impose a compactness assumption on the generalized kernel of the drift. Moreover, this control set is unique and contains the singularities of the drift in its closure.
A quantitative frequency-domain condition related to the exponential stabilizability for infinite-dimensional linear control systems is presented. It is proven that this condition is necessary and sufficient for the s...
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A quantitative frequency-domain condition related to the exponential stabilizability for infinite-dimensional linear control systems is presented. It is proven that this condition is necessary and sufficient for the stabilizability of special systems, while it is a necessary condition for the stabilizability in general. Applications are provided. (c) 2025 Elsevier Masson SAS. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
In this paper, we classify all the possible linear control systems on the homogeneous spaces of the 2D solvable Lie group and study their controllability and control sets. (c) 2022 Elsevier Inc. All rights reserved.
In this paper, we classify all the possible linear control systems on the homogeneous spaces of the 2D solvable Lie group and study their controllability and control sets. (c) 2022 Elsevier Inc. All rights reserved.
The large deviations of linearcontrol system trajectories from the equilibrium position during the stabilization process, known as peak-effect, represent a serious obstacle to the design of cascade controlsystems an...
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The large deviations of linearcontrol system trajectories from the equilibrium position during the stabilization process, known as peak-effect, represent a serious obstacle to the design of cascade controlsystems and to guidance stabilization. Evaluation of such deviations is an important problem not only for control theory but also for other branches of mathematics where similar phenomenon appears as, for example, in numerical analysis, in the study of hydrodynamic stability and transition to turbulence, in the dynamics of vehicular platoons, and many others. The aim of this paper is to improve one of the main results concerning upper bounds for the peak-effect in linear control systems in the work by B.T. Polyak and myself in 2016. As the lower bound for overshoot proved by R.N. Izmailov in 1987 shows, the asymptotic estimate for the upper bound obtained here cannot be improved.
In this note, we consider a uniformly completely controllable linear system. For this system, we show the existence of a linear state feedback such that the corresponding closed-loop system is kinematically equivalent...
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In this note, we consider a uniformly completely controllable linear system. For this system, we show the existence of a linear state feedback such that the corresponding closed-loop system is kinematically equivalent to a linear time-invariant system whose spectrum is a prior set of distinct real numbers.
The paper proposes a transition from a continuous control system with geometric and integral constraints to a discrete scheme. It is realized through partitioning the time interval and replacing the controls on the pa...
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In this paper, we study the dynamical behavior of a linearcontrol system on R-2 when the associated matrix has real eigenvalues. Different from the complex case, we show that the position of the control zero relative...
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In this paper, we study the dynamical behavior of a linearcontrol system on R-2 when the associated matrix has real eigenvalues. Different from the complex case, we show that the position of the control zero relative to the control range can have a strong interference in such dynamics if the matrix is not invertible. In the invertible case, we explicitly construct the unique control set with a nonempty interior.
This paper explicitly computes the unique control set D with the non-empty interior of a linearcontrol system on Double-struck capital R-2, when the associated matrix has complex eigenvalues. It turns out that the cl...
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This paper explicitly computes the unique control set D with the non-empty interior of a linearcontrol system on Double-struck capital R-2, when the associated matrix has complex eigenvalues. It turns out that the closure of D coincides with the region delimited by a computable periodic orbit O � of the system.
Let H denote the 3-dimensional Heisenberg Lie group. The present paper classify all possible linear control systems on the homogeneous spaces of H through its closed subgroups and expose a detailed study on the contro...
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