Network internal signal feedback and injection: Interconnection matrix redesign

Abstract

Abstract-The design of systems defined as networks (interconnections) of identical subsystems emerges as an interesting engineering problem, with some open issues. One of these issues is how to "retune" the interconnection in order to ensure the stability and the performance of the system. Based on the LFT representation and on the input-output framework, we propose in this paper some efficient "retuning" methods using convex optimization involving LMI constraints. The proposed approach can be interpreted as an extension of usual state space methods. Its application is investigated for the design of a network of PLLs.

Frequency Design of Interconnected Dissipative Systems: a Unified LMI Approach

“…The synchronisation problem of these PLL can be formulated as a weighted-H ∞ control problem. As noticed in [2], this requires the weighting function W (T s ) to be expressed as an LFT in T s .…”

“…In the particular case where interconnected systems are identical, a new paradigm has emerged, known as large-scale (distributed/decentralised) systems or homogeneous multi-agent systems approach. In the last decade, this approach has been successful in diverse areas of application such as formation flying [1], micro-Electronics [2], [3], biological networks [4], etc.…”

“…While the state-space approach can efficiently solve many standard problems, using especially Linear Matrix Inequalities (LMIs) [5], it appears to be more limited when considering interconnected complex systems. Many useful state-space results have then been extended to homogeneous LTI LFR systems [2], [4], [6], [7]. Nevertheless, there are still extended standard problems to solve.…”

Frequency Design of Lossless Passive Electronic Filters: A State-Space Formulation of the Direct Synthesis Approach

“…Constraint (1) can then be restated as follows: Find if (20) holds for all p(s), q(s), z 2 (s) and w 1 (s) that satisfy (19) for s = jω, ω ∈ Ω, and p(jω) = 1 jω • I q(jω). Applying Lemma 4 leads to check:…”

Systematic Design Method of Passive Ladder Filters using a Generalised Variable

“…The underlying idea is the introduction of a generalised variable which encompasses the information pertaining to the structure. In the last decade, this approach has been successful in many areas of applications as diverse as formation flying [9], micro-Electronics [10], [11], biological networks [12]. Our purpose is to apply this idea to the design of structured passive filters.…”