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We present a new stability condition for linear time-delay systems (TDS) with multiple incommensurate delays based on the Rekasius substitution and positive polynomials. The condition is checked by testing the positivity of multivariate polynomials in certain domains. For this purpose, we propose two alternative algorithms based on linear programming and sum of squares methods, respectively. The efficiency...
In this paper, we present a new sufficient stability condition for linear time-invariant multiple time-delay systems (MTDS) based on the Rekasius substitution and linear programming. The main advantage of the new stability condition is that it is applicable to the general case of multiple, incommensurate delays yet numerically tractable. In particular, using efficient linear programming algorithms,...
In this paper, a new delay-dependent stability analysis for time-delay linear time-invariant (TDLTI) systems is derived. In contrast to many recent approaches, which often utilize Lyapunov-Krasovskii functionals and linear matrix inequalities, an alternative approach is proposed in this paper. The proposed stability analysis is formulated in the frequency domain and investigates the characteristic...
This paper presents an observer for the class of nonlinear time-delay systems. The proposed observer is based on recent results in extended Kalman filtering for the class of deterministic nonlinear systems. However, the observer differs from the extended Kalman filter (EKF) by an additional term in the Riccati differential equation that takes the delayed states of the system into account. By using...
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