Abstract
The successive approximation Linear Parameter Varying systems subspace identification algorithm for discrete-time systems is based on a convergent sequence of linear time invariant deterministic-stochastic state-space approximations. In this chapter, this method is modified to cope with continuous-time LPV state-space models. To do this, the LPV system is discretised, the discrete-time model is identified by the successive approximations algorithm and then converted to a continuous-time model. Since affine dependence is preserved only for fast sampling, a subspace downsampling approach is used to estimate the linear time invariant deterministic-stochastic state-space approximations. A second order simulation example, with complex poles, illustrates the effectiveness of the new algorithm. © 2012 by World Scientific Publishing Co. Pte. Ltd.

Abstract

Abstract
The fitting of a causal dynamic model to an image is a fundamental problem in image processing, pattern recognition, and computer vision. There are numerous other applications that require a causal dynamic model, such as in scene analysis, machined parts inspection, and biometric analysis, to name only a few. There are many types of causal dynamic models that have been proposed in the literature, among which the autoregressive moving average (ARMA) and state-space models are the most widely known. In this paper we introduce a 2-D stochastic state-space system identification algorithm for obtaining stochastic 2-D, causal, recursive, and separable-in-denominator (CRSD) models in the Roesser state-space form. The algorithm is tested with a real image and the reconstructed image is shown to be almost indistinguishable to the true image.

Abstract
In this paper, the class of subspace system identification algorithms is used to derive a new identification algorithm for 2-D causal, recursive, and separable-in-denominator (CRSD) state space systems in the Roesser model form. The algorithm take a given deterministic input-output pair of 2-D signals and computes the system order (n) and system parameter matrices {A, B, C, D}. Since the CRSD model can be treated as two 1-D systems, the proposed algorithm first separates the vertical component from the state and output equations and then formulates an equivalent set of 1-D horizontal subspace equations. The solution to the horizontal subspace identification subproblem contains all the information necessary to compute the system order and parameter matrices, including those from the vertical subsystem.

Abstract
This article presents a new indirect identification method for continuous-time systems able to resolve the problem of fast sampling. To do this, a Subspace IDentification Down-Sampling (SIDDS) approach that takes into consideration the intermediate sampling instants of the input signal is proposed. This is done by partitioning the data set into m subsets, where m is the downsampling factor. Then, the discrete-time model is identified using a based subspace identification discrete-time algorithm where the data subsets are fused into a single one. Using the algebraic properties of the system, some of the parameters of the continuous-time model are directly estimated. A procedure that secures a prescribed number of zeros for the continuous-time model is used during the estimation process. The algorithm's performance is illustrated through an example of fast sampling, where its performance is compared with the direct methods implemented in Contsid.

Abstract