This document shows a dwell time-based switching technique for affine linear systems. The affine system is defined as a parameter dependent homotopic combination of two base modes, where the intermediate modes create an “artificial” grid of subsystems, producing lower dwell times estimates, specially when the number of modes increases. In some practical applications, the interpolated modes may replace previously designed or existing modes over a defined variable or range. Finsler's lemma is used to develop a relaxed Lyapunov-based condition that ensures the stability of the switched system and reduces the computation time of the developed technique. A user-defined parameter is used to influence the dwell time estimation. Numerical calculations performed over a switched system derived from an adaptive vibration attenuation controller shows the effectiveness of the proposed algorithm.

This paper considers the robust observer design problem for linear time-invariant dynamic systems subject to external disturbances. In this paper, robustness against disturbances is considered within a finite frequency range, instead of the standard infinite frequency range solution; this is achieved via the well established Generalized Kalman-Yakubovich-Popov (GKYP) results. In order to obtain a convex optimization problem, Finsler's Lemma is used to pose the GKYP Lemma as minimization problem in the form of a Linear Matrix Inequality which represents a finite range version of the Bounded Real Lemma. In contrast to other GKYP LMI formulations, the results presented in this work may be considered more conservative, but may be argued to be more simple and tractable than existing formulations. The effectiveness of the proposed procedure is shown through a simulation example.