H_∞Control And Robust Filtering Design For Uncertain Discrete Linear System

As an active research task, H_∞control and robust filtering design for uncertaindiscrete linear system play an important role in control fields. Due to the importance, ithas drawn large numbers of researchs’ attention to study the problems by proposingdifferent methods, and lots of valuble results are obtained. By developing newLyapunov function and controller that are constructed by a kind of matrix function, andusing method of linear matrix inquality (LMI for abbreviation), the conditions of H_∞control and robust filtering design are solved by applying methods of introducingvariables and iteration algorithm, which can further reduce conservatism.For state feedback H_∞control, this paper can be seen as an extension of previousone and the aim is to accelerate the convergence rate by using new Lyapunov functionand controller. To do so, the slack variables in this paper are introduced for the currenttime parameter and next time parameter respectively, which is different from othermethods where the variables are only introduced for the current time parameter, andthus leads to less conservative results. In the end, two examples are given todemonstrate the effectiveness of the proposed approach.For robust filtering design, designing methods are respectively given in terms of H_∞filter for1-D and H2filter for2-D. The first method is based on the idea of introducinghomogeneous polynomial parameter-dependent matrix function, and variablesintroduced and Lyapunov function are polynomial parameter-dependent. As the degreeof matrix function increases more variables are generated leading to less conservativeresults. However, the degree can not go infinitely and there exists supremum. When thedegree arrives at the supremum, the conservatism can not be further reduce and alsoincrease the complexity of the calculation. In order to further reduce the conservatism,given initial conditions, the second method is that the iterative algorithm is constructedto design filter. Compared with previous works, free matrix variables introduced in theiterative algorithm do not need to satisfy specific structure, and thus be able toeffectively reduce conservatism. Finally, simulation results demonstrate theeffectiveness of the proposed algorithm.