Balanced realization of stable transfer function matrices

Simple formulas are presented to compute the internally balanced minimal realization and the singular decomposition of the Hankel operator of a given continuous-time p×m stable transfer function matrix E(s)/d(s). The proposed formulas involve the Schwarz numbers of d(s) and the singular eigenvalues-eigenmatrices of a suitable finite matrix. Similar results are also obtained for a given discrete-time transfer function matrix     

Numerical inversion of a class of Laplace transforms

Simple formulas are derived to invert a class of Laplace transforms and compute the maximum absolute error. Uniform convergence, simultaneously in the t and s domain is achieved by selecting the approximant's free parameters.     

Internally balanced minimal realization of discrete SISO systems

Given the transfer function or the state equations in phase canonical form of a discrete SISO system, a method is proposed to obtain an internally balanced state-space representation of it.     

On the selection of the reduced order via balanced state representations

It is shown that a conjecture concerning actual and internal dominance advanced in a previous publication is not in general true. Thus, use of the second-order modes only to select the order of a given SISO high-order system'sHreduced approximant may lead to unsatisfactory results. It is then proposed to use instead certain formulas giving the impulse response energy and the steady-state step response ofH.     

Stability equation method to reduce the order of fast oscillating systems

A method for linear order reduction is proposed which, for fast oscillating systems, is superior to a number of other techniques (stability equation method, classic Padé technique etc.). For low-frequency systems the proposed method and the stability equation method yield identical results.     

Suboptimal control with incomplete state feedback

A simple method is presented to compute a suboptimal partial-state-feedback control law, based on a suitable approximation of the optimal complete-state-feedback case. A parameter is also available to stabilise the resulting closed-loop system.     

Direct method of reducing order of linear systems using koenig's theorem

Linear-system reduction is achieved by a simple and direct method based on Koenig's theorem, to approximate the stability equations of the given system. Thus the proposed technique is superior, for very high-order systems, to other methods which, yielding almost identical results, factorise the stability equations.     

Modification of Schwarz approximation

The state-space Schwarz approximation method is modified so that the original and the derived reduced model have an identical combination of their first time moments and Markov parameters. The proposed modification is in fact a state-space formulation of a frequency-domain method, which has appeared in previous publications.     

Minimal realization of transfer function matrices via oneorthogonal transformation

The minimal realization of a given arbitrary transfer function matrix G(s) is obtained by applying one orthogonal similarity transformation to the controllable realization of G( s). The similarity transformation is derived by computing the QR or the singular value decomposition of a matrix constructed from the coefficients of G(s). It is emphasized that the procedure has not been proved to be numerically stable. Moreover, the matrix to be decomposed is larger than the matrices factorized during the step-by-step procedures given