On Structured Realizability and Stabilizability of Linear Systems

We study the notion of structured realizability for linear systems defined over graphs. A stabilizable and detectable realization is structured if the state-space matrices inherit the sparsity pattern of the adjacency matrix of the associated graph. In this paper, we demonstrate that not every structured transfer matrix has a structured realization and we reveal the practical meaning of this fact. We also uncover a close connection between the structured realizability of a plant and whether the plant can be stabilized by a structured controller. In particular, we show that a structured stabilizing controller can only exist when the plant admits a structured realization. Finally, we give a parameterization of all structured stabilizing controllers and show that they always have structured realizations

Weak Resilience of Networked Control Systems

In this paper, we propose a method to establish a networked control system that maintains its stability in the presence of certain undesirable incidents on local controllers. We call such networked control systems weakly resilient. We first derive a necessary and sufficient condition for the weak resilience of networked systems. Networked systems do not generally satisfy this condition. Therefore, we provide a method for designing a compensator which ensures the weak resilience of the compensated system. Finally, we illustrate the efficiency of the proposed method by a power system example based on the IEEE 14-bus test system

Optimal Control of Two-Player Systems with Output Feedback

In this article, we consider a fundamental decentralized optimal control problem, which we call the two-player problem. Two subsystems are interconnected in a nested information pattern, and output feedback controllers must be designed for each subsystem. Several special cases of this architecture have previously been solved, such as the state-feedback case or the case where the dynamics of both systems are decoupled. In this paper, we present a detailed solution to the general case. The structure of the optimal decentralized controller is reminiscent of that of the optimal centralized controller; each player must estimate the state of the system given their available information and apply static control policies to these estimates to compute the optimal controller. The previously solved cases benefit from a separation between estimation and control which allows one to compute the control and estimation gains separately. This feature is not present in general, and some of the gains must be solved for simultaneously. We show that computing the required coupled estimation and control gains amounts to solving a small system of linear equations

A fractional representation approach to the robust regulation problem for MIMO systems

The aim of this paper is in developing unifying frequency domain theory for robust regulation of MIMO systems. The main theoretical results achieved are a new formulation of the internal model principle, solvability conditions for the robust regulation problem, and a parametrization of all robustly regulating controllers. The main results are formulated with minimal assumptions and without using coprime factorizations thus guaranteeing applicability with a very general class of systems. In addition to theoretical results, the design of robust controllers is addressed. The results are illustrated by two examples involving a delay and a heat equation.Comment: 23 pages, 3 figures, submitted to International Journal of Robust and Nonlinear Contro

3 sampled-data control of nonlinear systems

This chapter provides some of the main ideas resulting from recent developments in sampled-data control of nonlinear systems. We have tried to bring the basic parts of the new developments within the comfortable grasp of graduate students. Instead of presenting the more general results that are available in the literature, we opted to present their less general versions that are easier to understand and whose proofs are easier to follow. We note that some of the proofs we present have not appeared in the literature in this simplified form. Hence, we believe that this chapter will serve as an important reference for students and researchers that are willing to learn about this area of research

Voltage stabilization in DC microgrids: an approach based on line-independent plug-and-play controllers

We consider the problem of stabilizing voltages in DC microGrids (mGs) given by the interconnection of Distributed Generation Units (DGUs), power lines and loads. We propose a decentralized control architecture where the primary controller of each DGU can be designed in a Plug-and-Play (PnP) fashion, allowing the seamless addition of new DGUs. Differently from several other approaches to primary control, local design is independent of the parameters of power lines. Moreover, differently from the PnP control scheme in [1], the plug-in of a DGU does not require to update controllers of neighboring DGUs. Local control design is cast into a Linear Matrix Inequality (LMI) problem that, if unfeasible, allows one to deny plug-in requests that might be dangerous for mG stability. The proof of closed-loop stability of voltages exploits structured Lyapunov functions, the LaSalle invariance theorem and properties of graph Laplacians. Theoretical results are backed up by simulations in PSCAD