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.

This paper presents conditions to assure the mean-square stability of linear parameter-varying systems with Markov jumps. The model dynamics are driven not only by a Markov chain but also by time-varying parameters that take values in a polytopic set. No assumption is imposed on how the parameters vary within the polytopic set, i.e., the variation rate can be arbitrarily fast. The proposed conditions stem from a homogeneous polynomial Lyapunov function in the state space, adapted to account for Markov jumps. The stability certificate is sought through linear matrix inequalities. Numerical examples illustrate the paper's contribution.

A compression method, based on the choice of a wavelet that minimizes the distortion of compression for each electrocardiogram considered, is proposed in this paper. The scaling filter used on the determination of the wavelet function is obtained from the resolution of an optimization problem, which is unconstrained since the scaling filter is parametrized in a way that the constraints applied to the scaling filter are embedded on the parameters. The coefficients of projection of the signal over the wavelet subspaces are calculated and only the most significant ones are retained, being the significant coefficients determined in order to satisfy a pre-specified distortion measure. The bitmap that informs the positions of the retained coefficients is encoded along with the values of the coefficients by using an improved version of the Run Length Encoding technique. Experiments that compare the proposed approach with other techniques illustrate the efficiency of the method.