Zbigniew Bartosiewicz

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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)
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)
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)
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