Ewa Pawluszewicz

Realizations of Nonlinear Control Systems on Time Scales

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 of realizability of continuous-time polynomial systems. A simple construction of a realization is provided.

Control systems on regular time scales and their differential rings

The paper describes an algebraic construction of the inversive differential ring, associated with a nonlinear control system, defined on a nonhomogeneous but regular time scale. The ring of meromorphic functions in system variables is constructed under the assumption that the system is submersive, and equipped with three operators (delta- and nabla-derivatives, and the forward shift operator) whose properties are studied. The formalism developed unifies the existing theories for continuous- and discrete-time nonlinear systems, and accommodates also the case of non-uniformly sampled systems. Compared with the homogeneous case the main difficulties are noncommutativity of delta (nabla) derivative and shift operators and the fact that the additional time variable t appears in the definition of the differential ring. The latter yields that the new variables of the inversive closure, depending on t, have to be chosen to be smooth at each dense point t of the time scale.

Avoidance Control on Time Scales

We consider dynamic systems on time scales under the control of two agents. One of the agents desires to keep the state of the system out of a given set regardless of the other agent’s actions. Leitmann’s avoidance conditions are proved to be valid for dynamic systems evolving on an arbitrary time scale.

Stability of nonlinear

In the paper we study the subject of stability of systems with

h

h

-difference systems with

-differences of Caputo-, Riemann-Liouville- and Grunwald-Letnikov-type with

n

n

fractional orders

fractional orders. The equivalent descriptions of fractional

Fractional discrete-time linear control systems with initialisation

h

Linear Input-Output Equivalence and Row Reducedness of Discrete-Time Nonlinear Systems

-difference systems are presented. The sufficient conditions for asymptotic stability are given. Moreover, the Lyapunov direct method is used to analyze the stability of the considered systems with