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2 Przegląd Elektrotechniczny

2 2019

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Numerical methods for solving the modified filter algebraic riccati Elquation for H-infinity filtering

Horváth Zsolt

Przegląd Elektrotechniczny

2019

R. 95, nr 4

9--15

This paper presents numerical methods for solving the Modified Filter Algebraic Riccati Equation (MFARE) for synthesis of H-infinity fault detection filters. Two methods are presented, namely the gamma-iteration and then rewriting the MFARE in Linear Matrix Inequalities (LMIs) and casting it as a convex optimization problem. Each algorithm has to ensure the condition for a global convergence and also has to deliver an optimal solution. Not at least the computational cost has to be as small as possible.

Zaprezentowano metodę numeryczną rozwiązywania równania MFARE (Modified Filter Algebraic Riccati Equation). Badano dwie metody – iterację gamma i przepisywanie równania w postać Linear Matrix Inequantities.

Determining the dwell time constraint for switched H filters

Horváth Zsolt, Edelmayer András

Przegląd Elektrotechniczny

2019

R. 95, nr 1

7--11

This paper presents an algorithm for determining the minimum dwell time constraint for switched linear H fault detection filters. When applying switched systems, ensuring the stability is a crucial part, which can be guaranteed, when we switch slowly enough between the subsystems, more precisely the intervals between two consecutive switching, called dwell time, are large enough. The problem formulation is based on multiple Lyapunov functions and is expressed through a special form of linear matrix inequities (LMIs), which include a nonlinear term with the dwell time. This represents a multivariable time dependent optimization problem. To solve this special formulated LMIs, we propose an algorithm, called T -iteration, which is a combination of the procedure of interval halving with an LMI solver. The results of the illustrative example suggest further benefits.

W artykule zaprezentowano algorytm do określania minium czasowego miedzy kolejnymi przełączeniami liniowego filtru do detekcji błędu H. Sformułowanie problemu bazuje na wielokrotnej funkcji Lapunva. Do rozwiązania tego problmu zaproponowano algorytm T -iteration który jest kombinacją procedury połówkowania intwerwału z wykorzystanie solvera LMI.