This work addresses novel Linear Matrix Inequality (LMI)-based conditions for thedesign of discrete-time state derivative feedback controllers. The main contribution of this work consists of an augmented discretized model formulated in terms of the state derivative, such that uncertain sampling periods and parametric uncertainties in polytopic form can be propagated from the original continuous-time state space representation. The resulting discrete-time model is composed of homogeneous polynomial matrices with parameters lying in the Cartesian product of simplexes, plus an additive norm-bounded term representing the residual discretization error. Moreover, the referred condition allows for the closed-loop poles allocation of the augmented system in a D-stable region. Finally, numerical simulations illustrate the effectiveness of the proposed method.
In this paper, an optimal guaranteed cost control strategy to stabilize discrete-time linear parameter-varying systems with bounded rates of variation is presented. Sufficient conditions for the synthesis of fixed gain and gain-scheduled guaranteed cost controllers are given in terms of two sets of linear matrix inequalities. The main advantage of the proposed conditions is to rely on the use of homogeneous polynomial parameter-dependent Lyapunov functions of arbitrary degree that allow to assess the stability of the closed-loop system under the prescribed bound on the rate of parameter variations. In order to make the approach feasible, linear matrix inequality relaxations based on Pólya's theorem are addressed. Finally, the effectiveness of the proposed design methods is illustrated through numerical examples.
This paper addresses an alternative for the synthesis of a discrete-time stabilizing controller, taking into account requirements of D-stability via Linear Matrix Inequalities (LMIs) with a certain scalar parameter. Considering continuous time systems with polytopic uncertainty, this paper contributes with an alternative to incorporate D-stability requirements in the H 2 and H ∞ discrete-time controller synthesis from continuous-time D-stable regions via Euler's approximation. From these design requirements, robust controllers were designed and implemented for a case study system of two cars connected through a spring.
Este ambiente, esta sendo desenvolvido como parte do Projeto PROSOFT [i], em desenvolvimento no PGCC da UFRGS. Dará condições ao Engenheiro de Software de utilizar todos os recursos da metodologia SADT [2], de forma fácil e amigável.
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