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Abstract: Linear constant-coefficients control systems with output on arbitrary time scales are studied. Kalman criteria of controllability and observability 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… (More)

Control theory consists of two parallel branches: in the first one time is continuous, in the second one – discrete. The statements in both theories are usually similar or even identical. This is true for linear as well for nonlinear systems. The language of time scales, created some 25 years ago by Stefan Hilger [2] in his Ph.D. thesis, seems to be an… (More)

- Zbigniew Bartosiewicz, BRONIS LAW JAKUBCZYK
- 1994

Dynamic feedback equivalence for discrete-time systems follows the continuous-time analog introduced by B.Jakubczyk. In dynamic feedback transformations current and past states and controls are used. We show that two systems are dynamically feedback equivalent iff their difference algebras are isomorphic. This is parallel to a theorem on equivalence of… (More)

- Zbigniew Bartosiewicz, E. Pawłuszewicz
- 2002

It is shown that a nonlinear continuous-time control system with output is externally dynamically linearizable if and only if its differential output universe is free. Some regularity conditions are assumed, but the system does not have to be observable. Using universes instead of algebras or fields is essential as they allow for substitutions and… (More)

We show that for any variational symmetry of the problem of the calculus of variations on time scales there exists a conserved quantity along the respective EulerLagrange extremals.

- Ülle Kotta, Zbigniew Bartosiewicz, Ewa Pawluszewicz, Malgorzata Wyrwas
- Systems & Control Letters
- 2009

The purpose of this paper is to present a necessary and sufficient condition for irreducibility of nonlinear input–output delta differential equations. The condition is presented in terms of the common left divisor of two differential polynomials describing the behaviour of the system defined on a homogenous time scale. The concept of reduction is… (More)

- Zbigniew Bartosiewicz, Ewa Pawluszewicz
- IEEE Trans. Automat. Contr.
- 2008

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 criteria… (More)

Linear constant-coefficients control systems with output on arbitrary time scales are studied. Kalman criteria of controllability and observability 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)

The purpose of this paper is to present a necessary and sufficient condition for irreducibility of nonlinear input-output delta differential equations. The condition is presented in terms of the common left factor of two differential polynomials describing the behaviour of the system defined on a homogenous time scale. Copyright c © 2007 IFAC