This paper presents a linear matrix inequality-based procedure for the design of state feedback current controllers that are robust to uncertainties on grid inductance for grid-connected converters with LCL filters. The state feedback control law includes the filter state variables, the states of resonant controllers, and considers also the delay from digital control implementation. As the main contribution here, the proposed strategy allows to deal with resonant controllers of arbitrary dimension, and provides results complying with IEEE Standard 1547 requirements. The control synthesis condition takes into account the assignment of the closed-loop eigenvalues in a circular region with radius r, located inside the unit circle, and the control design relies only on the choice of the value of the radius in the interval 0 <; r ≤ 1, providing all the state feedback gains in a simple and efficient procedure.

This brief presents a control strategy for Markov jump linear systems (MJLS) with no access to the Markov state (or mode). The controller is assumed to be in the linear state-feedback format and the aim of the control problem is to design a static mode-independent gain that minimizes a bound to the corresponding H ₂ -cost. This approach has a practical appeal since it is often difficult to measure or to estimate the actual operating mode. The result of the proposed method is compared with that of a previous design, and its usefulness is illustrated by an application that considers the velocity control of a DC motor device subject to abrupt failures that is modeled as an MJLS.

This technical note is concerned with the problem of reduced order robust H_∞ dynamic output feedback control design for uncertain continuous-time linear systems. The uncertain time-invariant parameters belong to a polytopic domain and affect all the system matrices. The search for a reduced-order controller is converted in a problem of static output feedback control design for an augmented system. To solve the problem, a two-stage linear matrix inequality (LMI) procedure is proposed. At the first step, a stabilizing state feedback scheduled controller with polynomial or rational dependence on the parameters is determined. This parameter-dependent state feedback controller is used at the second stage, which synthesizes the robust (parameter-independent) output feedback H_∞ dynamic controller. A homogeneous polynomially parameter-dependent Lyapunov function of arbitrary degree is used to assess closed-loop stability with a prescribed H_∞ attenuation level. As illustrated by numerical examples, the proposed method provides better results than other LMI based conditions from the literature.

The ROLMIP (Robust LMI Parser) is a toolbox specialized in control theory for uncertain linear systems, built to work under MATLAB jointly with YALMIP, to ease the programming of sufficient Linear Matrix Inequality (LMI) conditions that, if feasible, assure the validity of parameter-dependent LMIs in the entire set of uncertainty considered. This article presents the new version of the ROLMIP toolbox, which was completely remodeled to provide a high-level user-friendly interface to cope with distinct uncertain domains (hypercube and multi-simplex) and to treat time-varying parameters in discrete- and continuous-time. By means of simple commands, the user is able to define polynomial matrices as well as to describe the desired parameter-dependent LMIs in an easy way, considerably reducing the programming time to end up with implementable LMI conditions. Therefore, ROLMIP helps the popularization of the state-of-the-art robust control methods for uncertain systems based on LMIs among graduate students, researchers, and engineers in control systems.