— 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)
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)
Linear constant-coefficients control systems with output on arbitrary time scales are studied. Kalman criteria of controllability and observabil-ity are extended to such systems. The main problem is to find criteria for an abstract input/output map to have a realization as a system on the time scale. Two different characterizations of realizability are… (More)
Linear dynamic systems with output, evolving on the space R ∞ of infinite sequences, are studied. They are described by infinite systems of ∆-differential linear equations with row-finite matrices, for which time belongs to an arbitrary time scale. Such systems generalize discrete-time and continuous-time row-finite systems on R ∞ , studied earlier.… (More)
The problem of dynamic feedback equivalence of nonlinear control systems on time scales is studied. Time scale is a model of time. Two most important cases are the real line (continuous time) and the set of integers (discrete time). Control systems on time scales include continuous-time and discrete-time systems. The delta algebra of a nonlinear control… (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.
— Linear control systems defined on arbitrary time scales are studied. It is shown that the classical results on stabilization and detectability for linear continuous-time and discrete-time systems can be extended to systems on arbitrary time scales. These results depend on the exponential stability criteria, which are different for different time scales.… (More)
The realization problem of linear time-invariant control systems is extended to time scales. There is given an algorithm for finding a state-space description of the system given by i/o differential equations on time scale. The obtained results are similar to known results for continuous and discrete-time cases.