Robust l2-l∞ Filtering for Discrete-Time Delay Systems

The problem of robust l2-l∞ filtering for discrete-time system with interval time-varying delay and uncertainty is investigated, where the time delay and uncertainty considered are varying in a given interval and norm-bounded, respectively. The filtering problem based on the l2-l∞ performance is to design a filter such that the filtering error system is asymptotically stable with minimizing the peak value of the estimation error for all possible bounded energy disturbances. Firstly, sufficient l2-l∞ performance analysis condition is established in terms of linear matrix inequalities (LMIs) for discrete-time delay systems by utilizing reciprocally convex approach. Then a less conservative result is obtained by introducing some variables to decouple the Lyapunov matrices and the filtering error system matrices. Moreover, the robust l2-l∞ filter is designed for systems with time-varying delay and uncertainty. Finally, a numerical example is given to demonstrate the effectiveness of the filter design method

Robust filtering of linear time invariant systems by means of polynomial Lyapunov functions

Orientadores: Pedro Luis Dias Peres, Ricardo Coração de Leão Fontoura de OliveiraDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Este trabalho apresenta novas condições na forma de desigualdades matriciais lineares para a síntese de filtros robustos H2 e H¥ de ordem completa, para sistemas incertos, contínuos e discretos no tempo. Os parâmetros incertos invariantes no tempo pertencem a um politopo com vértices conhecidos. Graças à existência de um número maior de variáveis de folga e à utilização de relaxações baseadas em matrizes polinomiais homogêneas, desigualdades matriciais lineares podem ser obtidas das condições propostas para o projeto de filtros robustos, com desempenho superior aos métodos existentes. A superioridade e eficiência do método proposto para o projeto dos filtros robustos são ilustradas por meio de comparações numéricas e exemplos da literaturaAbstract: This work presents new convex optimization procedures for full order robust H2 and H? filter design for continuous and discrete-time uncertain linear systems. The time-invariant uncertain parameters are supposed to belong to a polytope with known vertices. Thanks to the use of a larger number of slack variables and homogeneous polynomial relaxations, linear matrix inequalities for the design of robust filters can be derived from the proposed conditions, outperforming the existingmethods. The superiority and efficiency of the proposed method for robust filter design are illustrated by means of numerical comparisons in benchmark examples from the literatureMestradoAutomaçãoMestre em Engenharia Elétric