Linear differential equations with measures as coefficients and the control theory
Local controllability of odd systems
Local small time controllability and attainability of a set for nonlinear control system
In the present paper, we study the problem of small-time local attainability (STLA) of a closed set. For doing this, we introduce a new concept of variations of the reachable set well adapted to a given closed set and prove a new attainability result for a general dynamical system. This provide our main result for nonlinear control systems. Some applications to linear and polynomial systems are discussed and STLA necessary and sufficient conditions are obtained when the considered set is a hyperplane....
Local small time controllability and attainability of a set for nonlinear control system
In the present paper, we study the problem of small-time local attainability (STLA) of a closed set. For doing this, we introduce a new concept of variations of the reachable set well adapted to a given closed set and prove a new attainability result for a general dynamical system. This provide our main result for nonlinear control systems. Some applications to linear and polynomial systems are discussed and STLA necessary and sufficient conditions are obtained when the considered set...
Locally positive nonlinear systems
The notion of locally positive nonlinear time-varying linear systems is introduced. Necessary and sufficient conditions for the local positiveness of nonlinear time-varying systems are established. The concept of local reachability in the direction of a cone is introduced, and sufficient conditions for local reachability in the direction of a cone of this class of nonlinear systems are presented.
Minimum energy control of fractional descriptor positive discrete-time linear systems
On exact solutions of a class of interval boundary value problems
In this article, we deal with the Boundary Value Problem (BVP) for linear ordinary differential equations, the coefficients and the boundary values of which are constant intervals. To solve this kind of interval BVP, we implement an approach that differs from commonly used ones. With this approach, the interval BVP is interpreted as a family of classical (real) BVPs. The set (bunch) of solutions of all these real BVPs we define to be the solution of the interval BVP. Therefore, the novelty of the...
On finitary linear systems
On genericity of complete controllability in the space of linear parametrized control systems
On local and global controllability
On the continuous dependence of trajectories of bilinear systems on controls and its applications
On the properties of reachability, observability, controllability, and constructibility of discrete-time positive time-invariant linear systems with aperiodic choice of the sampling instants.
Optimal control in linear systems without the condition of regular controllability
Polynomial Control Systems.
Positive 2D discrete-time linear Lyapunov systems
Two models of positive 2D discrete-time linear Lyapunov systems are introduced. For both the models necessary and sufficient conditions for positivity, asymptotic stability, reachability and observability are established. The discussion is illustrated with numerical examples.
Problems on semigroups and control.
Properties of reachability and almost reachability subspaces of implicit systems: The extension problem
Rational semimodules over the max-plus semiring and geometric approach to discrete event systems
We introduce rational semimodules over semirings whose addition is idempotent, like the max-plus semiring, in order to extend the geometric approach of linear control to discrete event systems. We say that a subsemimodule of the free semimodule over a semiring is rational if it has a generating family that is a rational subset of , being thought of as a monoid under the entrywise product. We show that for various semirings of max-plus type whose elements are integers, rational semimodules...
Reachability and controllability of time-variant discrete-time positive linear systems
Reachability and observability of linear systems over max-plus
This paper discusses the properties of reachability and observability for linear systems over the max-plus algebra. Working in the event-domain, the concept of asticity is used to develop conditions for weak reachability and weak observability. In the reachability problem, residuation is used to determine if a state is reachable and to generate the required control sequence to reach it. In the observability problem, residuation is used to estimate the state. Finally, as in the continuous-variable...