Search

This article deals with the stability analysis of Lure type systems through aperiodic sampled‐data control laws, where the nonlinearity is assumed to be both sector and slope restricted. The proposed method is based on the use of a new class of looped‐functionals, which depends on the nonlinearity and its slope, and on a generalized Lure type function, that is quadratic on both the states and the nonlinearity and has a Lure‐Postnikov integral term. On this basis, conditions in the form of linear matrix inequalities to certify global or regional asymptotic stability of the closed‐loop system are obtained. These conditions are then used in optimization problems for computing the maximum intersampling interval or the maximum sector bounds for which the stability of the sampled‐data closed‐loop system is guaranteed. Numerical examples to illustrate the results are provided. [ABSTRACT FROM AUTHOR]

In this research article, the proportional-resonant controllers (PR) are introduced to fulfil the increased demand for controllers aiming at the tracking and/or rejection of periodic signals with superior performance than conventional PID ones. The main characteristic of these controllers is the infinite gain in the frequency of interest, which can lead to stability problems and makes their design and tuning more complex. More precisely, this paper presents a systematic approach for the computation of PR controllers parameters based on a frequency response method, using stability margins and sensitivity functions as indicators of performance and stability for the controlled system. In addition, a combination with a phase-lead compensator is proposed to allow better performance in an augmented bandwidth. Finally, the effectiveness of the proposed method is demonstrated for different classes of processes found in typical control problems. [ABSTRACT FROM AUTHOR]