System-level, Input-output and New Parameterizations of Stabilizing Controllers, and Their Numerical Computation

It is known that the set of internally stabilizing controller $\mathcal{C}_{\text{stab}}$ is non-convex, but it admits convex characterizations using certain closed-loop maps: a classical result is the {Youla parameterization}, and two recent notions are the {system-level parameterization} (SLP) and the {input-output parameterization} (IOP). In this paper, we address the existence of new convex parameterizations and discuss potential tradeoffs of each parametrization in different scenarios. Our main contributions are: 1) We first reveal that only four groups of stable closed-loop transfer matrices are equivalent to internal stability: one of them is used in the SLP, another one is used in the IOP, and the other two are new, leading to two new convex parameterizations of $\mathcal{C}_{\text{stab}}$. 2) We then investigate the properties of these parameterizations after imposing the finite impulse response (FIR) approximation, revealing that the IOP has the best ability of approximating $\mathcal{C}_{\text{stab}}$ given FIR constraints. 3) These four parameterizations require no \emph{a priori} doubly-coprime factorization of the plant, but impose a set of equality constraints. However, these equality constraints will never be satisfied exactly in numerical computation. We prove that the IOP is numerically robust for open-loop stable plants, in the sense that small mismatches in the equality constraints do not compromise the closed-loop stability. The SLP is known to enjoy numerical robustness in the state feedback case; here, we show that numerical robustness of the four-block SLP controller requires case-by-case analysis in the general output feedback case.Comment: 20 pages; 5 figures. Added extensions on numerial computation and robustness of closed-loop parameterization

Reconfigurable Intelligent Surfaces: A signal processing perspective with wireless applications

Antenna array technology enables the directional transmission and reception of wireless signals for communication, localization, and sensing purposes. The signal processing algorithms that underpin it began to be developed several decades ago [1], but it was with the deployment of 5G wireless mobile networks that the technology became mainstream [2]. The number of antenna elements in the arrays of 5G base stations (BSs) and user devices can be measured on the order of hundreds and tens, respectively. As networks shift toward using higher-frequency bands, more antennas fit into a given aperture. For communication purposes, the arrays are harnessed to form beams in desired directions to improve the signal-to-noise ratio (SNR) and multiplex data signals in the spatial domain (to one or multiple devices) and to suppress interference by spatial filtering [2]. For localization purposes, these arrays are employed to maintain the SNR when operating across wider bandwidths, for angle-of-arrival estimation, and to separate multiple sources and scatterers [3]. The practical use of these features requires that each antenna array is equipped with well-designed signal processing algorithms