Related papers: Classifications of Linear Controlled Systems
In this paper, we discuss the classification problem for linear time-invariant multivariable systems without control. It turns out that the observability and stability are invariant for topological equivalent systems. Abstract results…
This paper is devoted to the study of controllability of linear systems on generalized Heisenberg groups. Some general necessary controllability conditions and some sufficient ones are provided. We introduce the notion of decoupled systems,…
It is well-known that the controllability of finite-dimensional nonlinear systems can be established by showing the controllability of the linearized system. However, this classical result does not generalize to infinite-dimensional…
We present sufficient conditions under which a given linear nonautonomous system and its nonlinear perturbation are topologically conjugated. Our conditions are of a very general form and provided that the nonlinear perturbations are…
The purposes of this paper are to classify lower triangular forms and to determine under what conditions a nonlinear system is equivalent to a specific type of lower triangular forms. According to the least multi-indices and the greatest…
We consider the problem of topological linearization of smooth (C infinity or real analytic) control systems, i.e. of their local equivalence to a linear controllable system via point-wise transformations on the state and the control…
Positive linear systems on arbitrary time scales are studied. The theory developed in the paper unifies and extends concepts and results known for continuous-time and discrete-time systems. A necessary and sufficient condition for a linear…
A notion of $L^p$-exact controllability is introduced for linear controlled (forward) stochastic differential equations, for which several sufficient conditions are established. Further, it is proved that the $L^p$-exact controllability,…
The questions of global topological, smooth and holomorphic classifications of the differential systems, defined by covering foliations, are considered. The received results are applied to nonautonomous linear differential systems and…
Linear systems on Lie groups are a natural generalization of linear system on Euclidian spaces. For such systems, this paper studies the properties of the maximal sets of approximate controllability.
For linear infinite systems the approximate controllability problem by control constraints is considered. Controllability conditions represented via system parameters are obtained. Partial differential control systems and control systems…
Distinguishability takes a crucial rule in studying observability of hybrid system such as switched system. Recently, for two linear systems, Lou and Si gave a condition not only necessary but also sufficient to the distinguishability of…
A linear system of difference equations and a nonlinear perturbation are considered, we obtain sufficient conditions to ensure the topological equivalence between them, namely, the linear part satisfies a property of dichotomy on the…
The objective of this paper is to study the controllability of discrete-time linear control systems in solvable Lie groups. In the special case of nilpotent Lie groups, a necessary and sufficient condition for controllability is…
This paper establishes $C^m$ topological equivalence of nonautonomous semilinear difference equation with its linearization and generalizes the obtained results to discrete random dynamical systems, considering both, global and local,…
This paper studies the structural controllability of a class of uncertain switched linear systems, where the parameters of subsystems state matrices are either unknown or zero. The structural controllability is a generalization of the…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
In this paper, a necessary and sufficient condition for the controllability of networked systems with heterogeneous dynamics is established where the nodes are higher dimensional linear time invariant systems and the network topology is…
We obtain sufficient conditions ensuring the topological equivalence of two perturbed difference linear systems whose linear part has a property of generalized exponential dichotomy. When the exponential dichotomy is verified, we obtain a…
In this paper we explicitly calculate the control sets associated with a linear control system on the two dimensional solvable Lie group. We show that a linear control system of such kind admits exactly one control set or infinite control…