Mohsen Zamani

On the zeros of blocked linear systems with single and mixed frequency data

This paper studies properties of blocked systems resulting from blocking discrete linear systems with mixed frequency data. The focus is on the zeros of the blocked systems. We first establish results on the simpler single frequency case, where the unblocked linear systems have all data at the same frequency. In particular, an explicit relation between the system matrix of the unblocked linear systems and that of their corresponding blocked systems is derived. Based on this relation, it is shown that the blocked systems are zero free if and only if the related unblocked systems are zero free. Furthermore, it is illustrated that square systems have zeros generically, i.e. for generic parameter matrices, and the corresponding kernel is of dimension one. With the help of the results obtained for the single frequency case, we then identify a situation in which the blocked systems can be zero free.

Identifiability of regular and singular multivariate autoregressive models from mixed frequency data

This paper is concerned with identifiability of an underlying high frequency multivariate AR system from mixed frequency observations. Such problems arise for instance in economics when some variables are observed monthly whereas others are observed quarterly. If we have identifiability, the system and noise parameters and thus all second moments of the output process can be estimated consistently from mixed frequency data. Then linear least squares methods for forecasting and interpolating nonobserved output variables can be applied. Two ways for guaranteeing generic identifiability are discussed.

MULTIVARIATE AR SYSTEMS AND MIXED FREQUENCY DATA: G-IDENTIFIABILITY AND ESTIMATION

This paper is concerned with the problem of identifiability of the parameters of a high frequency multivariate autoregressive model from mixed frequency time series data. We demonstrate identifiability for generic parameter values using the population second moments of the observations. In addition we display a constructive algorithm for the parameter values and establish the continuity of the mapping attaching the high frequency parameters to these population second moments. These structural results are obtained using two alternative tools viz. extended Yule Walker equations and blocking of the output process. The cases of stock and flow variables, as well as of general linear transformations of high frequency data, are treated. Finally, we briefly discuss how our constructive identifiability results can be used for parameter estimation based on the sample second moments. (authors abstract)

On the Zero-Freeness of Tall Multirate Linear Systems

In this technical note, tall discrete-time linear systems with multirate outputs are studied. In particular, we focus on their zeros. In systems and control literature zeros of multirate systems are defined as those of their corresponding time-invariant systems obtained through blocking of the original multirate systems. We assume that blocked systems are tall, i.e., have more outputs than inputs. It is demonstrated that, for generic choice of the parameter matrices, linear systems with multirate outputs generically have no finite nonzero zeros. However, they may have zeros at the origin or at infinity depending on the choice of blocking delay and the input, state and output dimensions.

On the zeros of blocked time-invariant systems

Abstract This paper studies the zero properties of blocked linear systems resulting from blocking of linear time-invariant systems. The main idea is to establish a relation between the zero properties of blocked systems and the zero properties of their corresponding unblocked systems. In particular, it is shown that the blocked system has a zero if and only if the associated unblocked system has a zero. Furthermore, the zero properties of blocked systems under a generic setting i.e. a setting which parameter matrices A , B , C , D assume generic values, are examined. It is demonstrated that nonsquare blocked systems i.e. blocked systems with number of outputs unequal to the number of inputs, generically have no zeros; however, square blocked systems i.e. blocked systems with equal number of inputs and outputs, generically have only finite zeros and these finite zeros have geometric multiplicity one.

Zeros of networked systems with time-invariant interconnections

This paper studies zeros of networked linear systems with time-invariant interconnection topology. While the characterization of zeros is given for both heterogeneous and homogeneous networks, homogeneous networks are explored in greater detail. In the current paper, for homogeneous networks with time-invariant interconnection dynamics, it is illustrated how the zeros of each individual agents system description and zeros definable from the interconnection dynamics contribute to generating zeros of the whole network. We also demonstrate how zeros of networked systems and those of their associated blocked versions are related.

Zeros of networks of linear multi-agent systems: Time-invariant interconnections

This paper investigates the zero properties of networks of linear multi-agent control systems, where the coupling parameters between the agents are assumed to be constant. We characterize the zeros both for heterogeneous and homogeneous networks. Moreover, for homogenous networks with time-invariant interconnection dynamics and SISO agents, we illustrate how zeros of each individual agent and zeros of interconnection dynamics contribute to the zero properties of the whole network. We also investigate the effects of blocking on the zeros.

On the zero properties of linear discrete-time systems with multirate outputs

In this paper the zero properties of discrete-time linear systems with multirate outputs are studied. In the literature the zero properties of these systems are defined as those of their corresponding time-invariant blocked systems. Hence, the focus is on the zero properties of blocked systems resulting from blocking of linear systems with multirate outputs. In particular, we study the zero properties of tall blocked systems under a generic setting i.e. for generic parameter matrices; moreover, we only study the zero properties for choice of finite zeros. We demonstrate that tall blocked systems generically have no finite nonzero zeros. We then show when tall blocked systems can generically be zero-free at the origin i.e. Z = 0, and when they must have zeros at that point.

On the properties of linear multirate systems with coprime output rates

This paper studies discrete-time linear systems with multirate outputs, assuming that two measured output streams are available at coprime rates. In the literature this type of system, which can be considered as periodic time-varying, is commonly studied in its blocked version, since the well-known techniques of analysis developed for linear time-invariant systems can be used. In particular, we focus on some structural properties of the blocked systems and we prove that, under a generic setting i.e. for a generic choice of parameter matrices, the blocked systems are minimal when the underlying multirate system is defined using a minimal dimension system. Moreover, we focus on zeros of tall blocked systems i.e. blocked systems with more outputs than inputs. In particular, we study those cases where the associated system matrix attains full-column rank. We exhibit situations where they generically have no finite nonzero zeros.

Distributed Kalman filter in a network of linear systems

Abstract This paper is concerned with the problem of distributed Kalman filtering in a network of interconnected subsystems with distributed control protocols. We consider networks, which can be either homogeneous or heterogeneous, of linear time-invariant subsystems, given in the state-space form. We propose a distributed Kalman filtering scheme for this setup. The proposed method provides, at each node, an estimation of the state parameter, only based on locally available measurements and those from the neighbor nodes. The special feature of this method is that it exploits the particular structure of the considered network to obtain an estimate using only one prediction/update step at each time step. We show that the estimate produced by the proposed method asymptotically approaches that of the centralized Kalman filter, i.e., the optimal one with global knowledge of all network parameters, and we are able to bound the convergence rate. Moreover, if the initial states of all subsystems are mutually uncorrelated, the estimates of these two schemes are identical at each time step.