An Algorithm for the Calculation of the Dwell Time Constraint for Switched ℋ_∞ Filters

This paper presents a numerical 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 target, which can be guaranteed, when we switch slowly enough between the subsystems, more precisely when the intervals between two consecutive switching instants, 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 inequalities (LMIs), which include a nonlinear term of the dwell time. This represents a multivariable, time dependent optimization problem. As a result, the task cannot be treated as a simple feasibility problem involving a LMI solver as it is widely used in applications of the linear control. To solve these special LMIs, we propose a numerical algorithm, called 𝒯_d-iteration, which combines the procedure of interval halving with an LMI solver. The algorithm implemented in MATLAB shows its applicability as well as suggest further benefits for the switched linear control and filter synthesis.