Robust stability of discrete-time systems

A new approach is proposed for determining the robust stability of discrete-time systems where each coefficient of the characteristic polynomial can take any value between specified lower and upper bounds. It is based on the use of Rouche's theorem in the theory of complex variables.     

Use of singular value decomposition in system identification

Use of the singular value decomposition is suggested for problems of linear least-squares system identification rather than the usual method involving the normal equations.     

Determination of system-matrices of linear continuous-time multivariable systems from discrete-time models

It is shown that the computed system matrix for a continuous-time multivariable system may have the imaginary parts of its eigenvalues shifted from their true values when the matrix is determined from a discrete-time model. The same type of eigenvalue shift also can occur if a kth root of a matrix is used in the system identification. A numerical example is given to show that either predicted eigenvalue shift can occur. A bound on the sampling interval is suggested to avoid eigenvalue shifts.<>     

Reduced-order aggregated models for bilinear time-invariant dynamical systems

A necessary and sufficient condition for a bilinear time-invariant dynamical system to admit an aggregated reduced-order bilinear model is given.     

A comparison of the balanced matrix method and the aggregation method of model reduction

The balanced matrix method and the aggregation method for model reduction are compared. It is shown that there is a "natural" choice for the aggregated reduced model output matrix that makes the aggregated model comparable to the balanced matrix reduced-order model. This assumes that the eigenvalues retained in the aggregated model are truly dominant and that the orders of the two models are equal. However, there are situations in which the choice of the eigenvalues to be retained in an aggregated model is not obvious. In these cases the balanced matrix method may be superior. The models are compared in two numerical examples.     

Algorithm for the identification of continuous-time multivariable systems from their discrete-time models

A computationally efficient algorithm is given for estimating the state-space model of a continuous-time multivariable system from data obtained with a discrete-time model.     

Transformation algorithm for identification of continuous-time multivariable systems from discrete data

The problem of estimation of the state-space model of a multivariable continuous-time system based on the observation of sampled input-output data is considered. The letter deals mainly with the determination of the continuous-time model from a linear discrete-time model estimated from the observations.     

Identification of linear continuous-time multivariable systems using linear multistep methods

It is shown that linear multistep methods, commonly used to integrate ordinary differential equations numerically, can be used for the identification of linear continuous-time multivariable systems from samples of input/output data. An example problem is given to illustrate the use of multistep methods in system identification, and the results are compared with those obtained by the use of a discrete-time model.<>