Discussion on: “Measurable Signal Decoupling with Dynamic Feedforward Compensation and Unknown-input Observation for Systems with Direct Feedthrough”

Abstract

In the last four decades, ever since the seminal work of Basile and Marro [1] and Wonham and Morse [6], research efforts have been devoted to analysis and synthesis problems for linear state space systems within the well-known context of the geometric approach. The central issue in this approach is to use basic linear algebraic concepts such as linear mapping and linear subspace to investigate the structural properties of linear systems in terms of properties of the mappings A, B, C, D, etc., appearing in the system equations. For example, properties such as controllability, observability, stabilizability, and detectability can be expressed and characterized very effectively in terms of subspaces generated by these system mappings. Also, important notions such as system invertibility, system zeroes, minimum phase, weak observabilty, and strong controllability are analysed most naturally using the geometric approach. In addition, a large number of synthesis problems has been studied in this framework, such as pole placement and stabilization, observer design, disturbance decoupling by static state feedback or dynamic measurement feedback, observer design in the presence of unknown inputs, problems of output decoupling, problems of tracking and regulation, input-output decoupling, and decentralized control problems. Starting with the famous textbook by W.M. Wonham [7], a treatment of most of these synthesis problems can be found in the textbooks [2] and [4]. In the eighties, the ’exact’ versions of many of these control synthesis problems were generalized to their ’approximative’ versions, resulting in ’high gain’ feedback design problems such as almost disturbance decoupling, almost input-output decoupling, etc., see [5]. Around that time research attention within the systems and control community had been shifted to a large extend to H2 and H∞ control. However, also in the context of H2 and H∞ control an important role continued to be played by problems of disturbance decoupling and almost disturbance decoupling, see e.g [4]. Although the intensity of research within the geometric approach has become less, there is still an active community that devotes attention to further developing the area. L. Ntogramatzidis, the author of the paper to be discussed in this note, is clearly an exponent of this community. In this note we intend to explain the contribution of the