Robust Filtering for Continuous-Time Uncertain Linear Fractional Transformation Systems

Robust H2 and H∞ Filter Design for Continuous‐time Uncertain Linear Fractional Transformation Systems via LMI

“…Numerical examples in section IV show the efficiency of the proposed method in comparison with methods in the literature. The results of this paper can be viewed as the continuous-time counterpart for the presented results in [12] and a technical extension of the presented method in [1]. Also note that the proposed method, can be used as feedback controller design if we change the augmented system (8) with the closed-loop realization of the uncertain system and the to be designed controller.…”

“…In this example, the optimization problem is a 127 × 127 LMI which has 3130 scalar decision variables, hence the number of decision variables for the method proposed in [1] is 3119 and this shows that the improvement of obtained guaranteed cost is achieved by small increase in the number of variables.…”

“…As mentioned in section I, using parameter dependent Lyapunov and auxiliary matrices, could play an important role in the conservatism reduction of the optimization problem, like the method used in [12] and [1] define quadratic-LFT parameter dependent structure for Lyapunov matrix Q, and parameter dependent structure for auxiliary matrices G, F, W , M and Z as:…”

“…In the method of [10], g represents the degree of homogeneous polynomials used as decision variables in the parameter-dependent LMIs. In this example, the optimization problem is a 71 × 71 LMI which has 808 scaler decision variables, hence the number of decision [5] 0.7496 0.8653 [10] (g=1) 0.7017 0.7208 [10] (g=2) 0.6964 0.6987 [1] 0.4934 0.5230 Optimization problem (43) 0.4920 0.5217 Worst case performance of designed filter 0.4859 0.4926 variables for the method proposed in [1] is 800 and this shows that the improvement of obtained guaranteed cost ∞ is achieved by small increase in the number of variables.…”

“…It is obvious that sufficient conditions lead to conservatism, thus many efforts have been made to reduce the conservativeness of the analysis and design methods for improving the systems performance, see e.g. [1,[5][6][7][8][9][10]12,14,15] and references therein.…”