Mert Bastug

Mert Bastug, Mihaly Petreczky, Rafael Wisniewski et al.

Two moment-matching methods for model reduction of linear switched systems (LSSs) are presented. The methods are similar to the Krylov subspace methods used for moment matching for linear systems. The more general one of the two methods, is based on the so called "nice selection" of some vectors in the reachability or observability space of the LSS. The underlying theory is closely related to the (partial) realization theory of LSSs. In this paper, the connection of the methods to the realization theory of LSSs is provided, and algorithms are developed for the purpose of model reduction. Conditions for applicability of the methods for model reduction are stated and finally the results are illustrated on numerical examples.

Mert Bastug, Mihaly Petreczky, Rafael Wisniewski et al.

We present a procedure for reducing the number of continuous states of discrete-time linear switched systems, such that the reduced system has the same behavior as the original system for a subset of switching sequences. The proposed method is expected to be useful for abstraction based control synthesis methods for hybrid systems.

Mert Bastug, Laurentiu Hetel, Mihaly Petreczky

Two approaches to moment matching based model reduction of aperiodically sampled data systems are given. The term "aperiodic sampling" is used in the paper to indicate that the time between two consecutive sampling instants can take its value from a pre-specified finite set of allowed sampling intervals. Such systems can be represented by discrete-time linear switched (LS) state space (SS) models. One of the approaches investigated in the paper is to apply model reduction by moment matching on the linear time-invariant (LTI) plant model, then compare the responses of the LS SS models acquired from the original and reduced order LTI plants. The second approach is to apply a moment matching based model reduction method on the LS SS model acquired from the original LTI plant, and then compare the responses of the original and reduced LS SS models. It is proven that for both methods, as long as the original LTI plant is stable, the resulting reduced order LS SS model of the sampled data system is quadratically stable. The results from two approaches are compared with numerical examples.

Mert Bastug, Mihaly Petreczky, Roland Toth et al.

We present a novel algorithm for reducing the state dimension, i.e. order, of linear parameter varying (LPV) discrete-time state-space (SS) models with affine dependence on the scheduling variable. The input-output behavior of the reduced order model approximates that of the original model. In fact, for input and scheduling sequences of a certain length, the input-output behaviors of the reduced and original model coincide. The proposed method can also be interpreted as a reachability and observability reduction (minimization) procedure for LPV-SS representations with affine dependence.