Abstract
We address the identification of discrete-time linear parameter varying systems in the state-space form with affine parameter dependence. In previous work, some of the authors have addressed this problem and an iterative algorithm that avoids the curse of dimensionality, inherent to this class of problems, was developed for the identification of multiple input multiple output systems. Although convergence of this algorithm has been assured for white noise sequences, it has also converged for other type of scheduling signals. Never less, its application is still not generalized to every class of scheduling parameters. In this paper, the algorithm is modified in order to identify multiple input single output systems with quasi-stationary scheduling signals. In every iteration, the system is modeled as a linear time invariant system driven by an extended input composed by the measured input, the Kronecker product between this signal and the scheduling parameter and the Kronecker product between the scheduling and the state estimated at the previous iteration. The remaining unknown signals are considered as "noise". Furthermore, the system is decomposed into a "deterministic" system driven by the known inputs and a "stochastic" subsystem driven by noise. The system is identified as a high order autoregressive exogeneous model. In order to whiten the noise, the input/output data is filtered by the inverse noise transfer function and a state-space model is estimated for the "deterministic" subsystem. Then, the output simulated by this system is subtracted from the measurements to obtain the output stochastic component. Finally, the state of the system is estimated using a Kalman filter and a deconvolution technique. Then, the state becomes an entry to the system for the next iteration, after being multiplied by the scheduling parameter. The whole process is repeated until convergence. The algorithm is tested using periodic scheduling signals and compared with other approaches developed by the same authors. © 2012 IFAC.

Abstract
This paper addresses the detection and classification of low amplitude signals within the QRS complex of the signal-averaged electrocardiogram. Linear and bilinear Kalman filter models are fitted using the subspace system identification family of algorithms. If the residuals from the models are a white noise process, then anything that cannot be modeled with the state-space models will show up in the residuals as low amplitude signal + noise. Diagnostic tests and analysis on the residuals will then lead to detection and classification of abnormalities in the intra-QRS complex. The end result is a diagnostic tool to aid the physician. © 2012 IFAC.

Abstract
In this paper we introduce a new identification algorithm for MIMO bilinear systems driven by white noise inputs. The new algorithm is based on a convergent sequence of linear deterministic-stochastic state space approximations, thus considered a Picard based method. The key to the algorithm is the fact that the bilinear terms behave like white noise processes. Using a linear Kalman filter, the bilinear terms can be estimated and combined with the system inputs at each iteration, leading to a linear system which can be identified with a linear-deterministic subspace algorithm such as MOESP, N4SID, or CVA. Furthermore, the model parameters obtained with the new algorithm converge to those of a bilinear model. Finally, the dimensions of the data matrices are comparable to those of a linear subspace algorithm, thus avoiding the curse of dimensionality.

Abstract
In this technical brief, a new subspace state space system identification algorithm for multi-input multi-output bilinear systems driven by white noise inputs is introduced. The new algorithm is based on a uniformly convergent Picard sequence of linear deterministic-stochastic state space subsystems which are easily identifiable by any linear deterministic-stochastic subspace algorithm such as MOESP, N4SID, CVA, or CCA. The key to the proposed algorithm is the fact that the bilinear term is a second-order white noise process. Using a standard linear Kalman filter model, the bilinear term can be estimated and combined with the system inputs at each iteration, thus leading to a linear system with extended inputs of dimension m(n + 1), where n is the system order and m is the dimension of the inputs. It is also shown that the model parameters obtained with the new algorithm converge to those of the true bilinear model. Moreover, the proposed algorithm has the same consistency conditions as the linear subspace identification algorithms when i -> infinity, where i is the number of block rows in the past/future block Hankel data matrices. Typical bilinear subspace identification algorithms available in the literature cannot handle large values of i, thus leading to biased parameter estimates. Unlike existing bilinear subspace identification algorithms whose row dimensions in the data matrices grow exponentially, and hence suffer from the "curse of dimensionality," in the proposed algorithm the dimensions of the data matrices are comparable to those of a linear subspace identification algorithm. A case study is presented with data from a heat exchanger experiment.

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