Minimal partial realizations in a canonical form

Abstract

Absfracf-A canonical realization for a partial sequence of real, a nstant matrices is obtained by identifying the system invariants defied by Popov [Ill. Further, the case where the mdting realization must also be stable is considered. The example used by Tether [q is solved, and the resnlts compared with those of Tether [5] and A c k e m [12].

Computation of Realizations Composed of Dynamic and Static Parts of Improper Transfer Matrices

“…Using one of the well-known methods (Christodoulou and Mertzios, 1985;Kaczorek, 1992;Kailath, 1980;Roman and Bullock, 1975;Sinha Naresk, 1975;Wolovich and Guidorsi, 1977), we can determine a minimal real-…”

“…There exist many well-known methods for the computation of minimal realizations for given proper and improper transfer matrices (Christodoulou and Mertzios, 1985;Kaczorek, 1992;Kailath, 1980;Roman and Bullock, 1975;Sinha Naresk, 1975;Wolovich and Guidorsi, 1977). It is also well known that a singular linear system described by static equations can be decomposed into two subsystems, a standard dynamical subsystem and a static subsystem (Kaczorek, 1992).…”

Minimal stable partial realization

“…Unfortunately this algorithm will not guarantee asymptotic stability of the realization even when it is known that the system giving rise to the Markov parameters is asymptotically stable. Efforts to include a stability constrant on this form of canonical realization are described in [16]. The algorithm presented can be implemented for relatively simple systems but would require further research effort to give a precise procedure to implement the various tests for higher order multivariable systems.…”

“…In exploring the application of decision methods to this problem, the objective is to minimize by analytic 'means, the number of unknowns in the underlying polynomial equalities and so minimize the complexity of the decision problem and thereby achieve more efficient solutions than could otherwise be obtained as in [16]. Proceeding towards the objective has been fruitful, both in defining a relevant simplified decision problem and in giving insight into the nature of the minimal order asymptotically stable partial realization problem itself.…”

Realization theory for two-time-scale distributions through approximation of Markov parameters

“…The question of minimality of a state space realization in terms of the Markov parameters of the system was investigated a few years later in the same decade by Kalman and Ho (1965). During the 1970s, algorithms for efficient computation of the minimal realization were developed and the question of the stability of the realization was addressed by several authors (Kalman and De Claris 1970, Thether 1970, Roman and Bullock 1975, Ledwich and Moore 1976. Much of the current literature deals with the problem of realizing a given system from a finite sequence of real numbers.…”