On computing minimal realizations of periodic descriptor systems
نویسنده
چکیده
We propose computationally efficient and numerically reliable algorithms to compute minimal realizations of periodic descriptor systems. The main computational tool employed for the structural analysis of periodic descriptor systems (i.e., reachability and observability) is the orthogonal reduction of periodic matrix pairs to Kronecker-like forms. Specializations of a general reduction algorithm are employed for particular type of systems. One of the proposed minimal realization methods relies exclusively on structure preserving manipulations via orthogonal transformations for which the backward numerical stability can be proved.
منابع مشابه
Determining the order of minimal realization of descriptor systems without use of the Weierstrass canonical form
A common method to determine the order of minimal realization of a continuous linear time invariant descriptor system is to decompose it into slow and fast subsystems using the Weierstrass canonical form. The Weierstrass decomposition should be avoided because it is generally an ill-conditioned problem that requires many complex calculations especially for high-dimensional systems. The present ...
متن کاملComputation of Minimal Realizations of Periodic Systems
We propose balancing related numerically reliable methods to compute minimal realizations of linear periodic systems with time-varying dimensions. The first 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 pote...
متن کاملGeneralized partial realizations
In this paper we extend Kalman's concept of partial realization and deene generalized partial realizations of nite matrix sequences by descriptor systems. Our deenition is in agreement with the realization theory for deterministic boundary value descriptor systems 15]. The aim of this contribution is to prove a counterpart of Kalman's main theorem of realization theory for generalized partial r...
متن کاملSquare-Root Balancing and Computation of Minimal Realizations of Periodic Systems
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...
متن کاملBalancing related methods for minimal realization of periodic systems
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...
متن کامل