Parameter dependent filter design for linear continuous-time uncertain systems with arbitrarily time-varying parameters in polytopic domains

Improved robust filter synthesis combining linear matrix inequalities and heuristic algorithms

“…The methodology proposed in this work consists in using HOA to find filter matrices A f , B fu , and B fy , and then solve the LMIs while keeping the entire structure of . (𝛼), G 12 (𝛼), G 21 (𝛼), and G 22 (𝛼) ∈ R n×n ; matrices Q 11 (𝛼) and Q 12 (𝛼) ∈ R n z ×n , F 11 (𝛼) and F 12 (𝛼) ∈ R n w ×n , R 11 (𝛼) and R 12 (𝛼) ∈ R n u ×n ; and also scalars 𝜏 and 𝛾 ∈ R + , then the matrices C f , D fu and D fy are elements of the robust filter (4), with guaranteed cost  ∞ from w(t) to e(t) given by 𝛾, if the following optimization problem is feasible…”

“…Filtering techniques are widely applied in control and monitoring systems to allow correct mensuration when noises and disturbances are noticed in the system, being also capable of estimating unavailable variables. With the popularization of Lyapunov's theorem, new and modern filtering techniques emerged, allowing their robust application in systems with uncertain parameters, 1,2 linear parameter varying (LPV), 3,4 and nonlinear structures. 5,6 Filtering problems usually involve uncertainties and additional performance indexes, such as the  2 and  ∞ norms.…”