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This paper provides a complete characterization of solvability of the problem of structural model matching by output feedback in linear impulsive systems with nonuniformly spaced state jumps. Namely, given a linear impulsive plant and a linear impulsive model, both subject to sequences of state jumps which are assumed to be simultaneous and measurable, the problem consists in finding a linear impulsive compensator that achieves exact matching between the respective forced responses of the linear impulsive plant and of the linear impulsive model, by means of a dynamic feedback of the plant output, for all the admissible input functions and for all the admissible sequences of jump times. The solution of the stated problem is achieved by reducing it to an equivalent problem of structural disturbance decoupling by dynamic feedforward. Indeed, this latter problem is formulated for the so-called extended linear impulsive system, which consists of a suitable connection between the given plant and a modified model. A necessary and sufficient condition for the solution of the structural disturbance decoupling problem is first shown. The proof of sufficiency is constructive, since it is based on the synthesis of the compensator that solves the problem. The proof of necessity is based on the definition and the geometric properties of the unobservable subspace of a linear impulsive system subject to unequally spaced state jumps. Finally, the equivalence between the two structural problems is formally established and proven.
In this paper we have described a new design algorithm for the whole set of latent-structure assignments via the approaches of block structure of λ-matrices placement. The procedure that has been developed is based on decoupling of the interactions between control loops in a multivariable plant. The procedure is performed using matrix polynomial solvent reconstruction for the decoupling purposes. However, for the design of the trajectory tracking controller, each input-output pair is treated respectively by designing SISO controllers. A second procedure is the MIMO PID compensator design via the model-matching method. This latter algorithm has been developed in order to avoid the internal or the hidden instability, which may occur in the first method, due to the block zeros - block poles cancellation.
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.
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