We propose balancing related numerically reliable methods to compute minimal realizations of linear periodic systems with time-varying dimensions. The rst method belongs to the family of square-root methods with guaranteed enhanced computational accuracy and can be used to compute balanced minimal order realizations. An alternative balancing-free square-root method has the advantage of a potent...

Minimal distance methods are simple and in some circumstances highly accurate. In this paper relations between neural and minimal distance methods are investigated. Neural realization facilitates new versions of minimal distance methods. Parametrization of distance functions, distance-based weighting of neighbors, active selection of reference vectors from the training set and relations to the ...

Reducing the amount of hardware needed for implementing a sequential machine is very important. The problem of, in the strict sense, minimal realization of sequential machines is difficult and it is entirely unsolved (except complete enumeration). Typically, this problem can be replaced with a number of subproblems such as: state minimization, state assignment, choice of flip-flops and minimiza...

We propose a numerically reliable approach for balancing and minimal realization of linear periodic systems with time-varying dimensions. The proposed approach to balancing belongs to the family of square-root methods with guaranteed enhanced computational accuracy and can be also used to compute balanced minimal order realizations from non-minimal ones. An alternative balancing-free square-roo...

The paper presents realization theory of discrete-time linear switched systems (abbreviated by DTLSSs). We present necessary and sufficient conditions for an input-output map to admit a discrete-time linear switched state-space realization. In addition, we present a characterization of minimality of discrete-time linear switched systems in terms of reachability and observability. Further, we pr...