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The paper addresses the problem of reducibility of nonlinear discrete-time systems, described by implicit higher order difference equations where no a priori distinction is made between input and output variables. The reducibility definition is based on the concept of autonomous element. We prove necessary reducibility condition, presented in terms of the left submodule, generated by the row matrix, describing the behavior of the linearized system, over the ring of left difference polynomials. Then the reducibility of the system implies the closedness of the submodule, like in the linear time-invariant case. In the special case, when the variables may be specified as inputs and outputs and the system equations are Niven in the explicit form, the results of this paper yield the known results.
Content available remote A note on model matching for nonrealizable nonlinear systems
In this technical note the model matching problem for nonlinear systems not admitting the state space realization is discussed. Both continuous- and discrete-time cases are addressed. It is demonstrated, by using a transfer function formalism, that even in case of nonrealizable systems it is sometimes still possible to find realizable compensators.
Content available remote Realization of nonlinear composite systems
The paper studies the realization problem for series and parallel connections of nonlinear single-input single-output systems, described by higher order differential equations. Necessary and sufficient conditions are given for the existence of the classical state space realization in both cases. It is proved that post- and parallel compensators are of no help in overcoming non-realizability. Results are illustrated by an example.
The paper proposed a control design method for servo-controlled pneumatic systems, which is based on the feedback linearization theory. The pneumatic actuator system model is transformed into a linear system description first by regular static state feedback and state coordinate transformation. A servo/tracking controller is then developed for the linear model. Since there exists an inverse transformation for the new co-ordinate system, the designed servo control is finally transformed back to the original state co-ordinates and input. Two different cases are discussed in the paper - the pneumatic cylinder is driven by a single five-port proportional valve and driven by two three-port proportional valves. At the initial stage, for the convenience of finding a suitable set of new co-ordinates, the static friction forces are ignored. The static friction forces can be treated as uncertainties to the system for robust controller design.
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