In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: σ-differential field a b s t r a c t The purpose of this paper is to present a… (More)
— Nonlinear partially defined systems on an arbitrary unbounded time scale are studied. They include continuous-time and discrete-time systems. The main problem is to find necessary and sufficient conditions for an abstract input/output map to have a realization as a nonlinear system of a specific class on the time scale. The obtained results extend… (More)
— An algebraic framework for discrete-time nonlin-ear control systems is introduced, based on the forward and backward shifts of the vector fields, dual to that based on differential 1-forms. As an application, the accessibility criterion of a control system in terms of vector fields is given and compared to those obtained under more restrictive assumptions.
— The fundamental problem of the calculus of variations on time scales concerns the minimization of a delta-integral over all trajectories satisfying given boundary conditions. In this paper we prove the second Euler-Lagrange necessary optimality condition for optimal trajectories of variational problems on time scales. As an example of application of the… (More)
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 system on a time scale to be positive is presented. Properties of positive reachable sets are investigated and… (More)