Zbigniew Bartosiewicz

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— 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)
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)
— 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)