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We study the problem of optimal reduced-dimension linear transform coding and reconstruction of a signal based on distributed correlated observations of the signal. In the mean square estimation context this involves finding the optimal signal representation based on multiple incomplete or only partial observations that are correlated. In particular, this leads to the study of finding the optimal Karhunen--Loeve basis based on the censored observations. The problem has been considered previously by Gastpar, Dragotti, and Vetterli in the context of jointly Gaussian random variables based on using conditional covariances. In this paper, we derive the estimation results in the more general setting of second-order random variables with arbitrary distributions, using entirely different techniques based on the idea of innovations. We explicitly solve the single transform coder case, give a characterization of optimality in the multiple distributed transform coders scenario and provide additional insights into the structure of the problem. Index Terms--Distributed signal processing, innovations, Karhunen-Loeve transform, optimal linear estimation.

The purpose of this paper is to formulate and solve a H[infinity] controller synthesis problem for a class of noncommutative linear stochastic systems which includes many examples of interest in quantum technology. The paper includes results on the class of such systems for which the quantum commutation relations are preserved (such a requirement must be satisfied in a physical quantum system). A quantum version of standard (classical) dissipativity results are presented and from this a quantum version of the Strict Bounded Real Lemma is derived. This enables a quantum version of the two Riccati solution to the H[infinity] control problem to be presented. This result leads to controllers which may be realized using purely quantum, purely classical or a mixture of quantum and classical elements. This issue of physical realizability of the controller is examined in detail, and necessary and sufficient conditions are given. Our results are constructive in the sense that we provide explicit formulas for the Hamiltonian function and coupling operator corresponding to the controller. Index Terms--[H.sup.[infinity]] robust control, dissipativity, quantum controller realization, quantum feedback control, quantum optics, strict bounded real lemma.

In this note, we study the rational covariance extension problem with degree bound when the chosen pseudopolynomial of degree at most n has zeros on the boundary of the unit circle and derive some new theoretical results for this special case. In particular, a necessary and sufficient condition for a solution to be bounded (i.e., has no poles on the unit circle) is established. Our approach is based on convex optimization, similar in spirit to the recent development of a theory of generalized interpolation with a complexity constraint. However, the two treatments do not proceed in the same way and there are important differences between them which we discuss herein. An implication of our results is that bounded solutions can be computed via methods that have been developed for pseudopolynomials which are free of zeros on the boundary, extending the utility of those methods. Numerical examples are provided for illustration. Index Terms--Boundary zeros, bounded solutions, Nevanlinna-Pick interpolation, poles and zeros, rational covariance extension.

This study compares two inverter control methods, virtual oscillator control (VOC) and droop control, in terms of time responses of a three-phase single-inverter system under a load step change. The analytical comparison is aided by small-signal modelling. Two small-signal VOC models are derived from the average VOC dynamics by approximating average power differently; two small-signal droop control models using distinct filters are also assessed. By letting the two controllers have similar droop characteristics in steady state, participation analyses are performed to predict transient responses of the systems. The analyses are verified by simulations and experiments. This study presents a meticulous comparison between VOC and droop control in a three-phase system. It is demonstrated that two types of linearized models produce similar transient responses in the output voltage and current amplitudes. VOC has a faster transient response in instantaneous frequency while the droop controller can have a transient response as fast as the VOC in the terminal voltage amplitude. This reveals that the VOC and droop controller can be designed to yield similar responses under a load disturbance. Comparing them in a standalone system aids in understanding the control loop as a step towards understanding transient behavior in multiple source systems. [ABSTRACT FROM AUTHOR]

Utilisation of variable distributed energy sources in a microgrid necessitates control of active power and is enhanced by the control of reactive power. A control technique to regulate the active and reactive power of a virtual oscillator controlled inverter is presented. Current feedback gain of the virtual oscillator controlled inverter is used to regulate the active or reactive power. In order to achieve the desired power set‐point, a PI controller is used to tune the current feedback gain. An approximate local stability analysis is presented using the system linearisation and eigenvalues analysis. Constraints on the virtual oscillator controller and system parameters are identified to ensure the stability of the system. Global stability of the system is investigated by determining a Lyapunov function using the sum‐of‐squares technique. Simulation and experimental results are presented for both the cases of active and reactive power control of a virtual oscillator controlled inverter to verify the analytical analysis and to demonstrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]