A Class Of Linear Parameter Varying Systems Variable Gain H_ ¡Þ Filtering

Motivated by robust H_∞ filtering theory and gain-scheduled H_∞ control theory, this thesis deals with the problem of gain-scheduled H_∞ filter design for a class of linear parameter-varying systems (LPV systems). The main results are as follows:Part I. A class of continuous-time LPV systems, which take the linear fractional transformation (LFT) structure, are studied. For this class of systems, the gain-scheduled H_∞ filtering problem is investigated in this part. By developing a linear matrix inequality (LMI) approach, a sufficient condition for the existence of the filter under consideration is obtained based on quadratic Lyapunov functions. This condition is given in terms of a set of LMIs. A desired gain-scheduled H_∞ filter can be constructed by solving the proposed LMIs. It is shown that the designed filter guarantees the asymptotic stability and H_∞ performance of the filtering error system. Finally, the application of the proposed design method is numerically demonstrate by simulation results.Part II. This part considers the gain-scheduled H_∞ filter design problem for a class of LPV systems being of non-linear fractional transformation (NFT) structure. By using the LMI approach and introducing a group of equations involving weighted matrices, we develop design methods for the gain-scheduled H_∞ filter based on parameter-dependent Lyapunov functions and quadratic Lyapunov functions, respectively. It is shown that the design results obtained based on parameter-dependent Lyapunov function approach are less conservative than the results obtained based on quadratic Lyapunov function approach. Finally, the application of the proposed design method is numerically demonstrate by simulation results.