Lyapunov Matrices for the Stability Analysis of a Multiple Distributed Time-Delay System with Repeated Piecewise Function Kernel

Resumen: In this publication, we construct the Lyapunov matrices of a multiple distributed time-delay system in the particular case where the kernel functions are repeated. The matrix construction is reduced to the computation of the solutions of a delay free system of matrix equations. We find that the number of auxiliary matrices which allow us to find the solutions can be significantly reduced. We also carry out a stability analysis with the help of the obtained Lyapunov matrix. Two illustrative examples are presented.

¿Cómo citar?

Luis Juárez & Sabine Mondié. Lyapunov Matrices for the Stability Analysis of a Multiple Distributed Time-Delay System with Repeated Piecewise Function Kernel. Memorias del Congreso Nacional de Control Automático, pp. 290-295, 2018.

Palabras clave

Time-delay, Linear systems, Stability analysis, Lyapunov stability

• Aliseyko, A. (2017). Lyapunov matrices for a class of time-delay systems with piecewise-constant kernel. International Journal of Control, 1–8.
• Cuvas, C., Mondi´e, S., and Ochoa, G. (2015). Distributed delay systems with truncated gamma distribution: instability regions. IFAC-PapersOnLine, 48(12), 239– 244.
• Egorov, A.V., Cuvas, C., and Mondi´e, S. (2017). Necessary and sufficient stability conditions for linear systems with pointwise and distributed delays. Automatica, 80, 218–224.
• Garcia-Lozano, H. and Kharitonov, V.L. (2004). Lyapunov matrices for time delay system with commensurate delays. IFAC Proceedings Volumes, 37(21), 91–95.
• Huesca, E., Mondi´e, S., and Santos, O. (2009). Polynomial approximations of the Lyapunov matrix of a class of time delay systems. IFAC Proceedings Volumes, 42(14), 261–266.
• Jarlebring, E., Vanbiervliet, J., and Michiels, W. (2009). Characterizing and computing the H2 norm of timedelay systems by solving the delay lyapunov equation.
• Kharitonov, V.L. (2006). Lyapunov matrices for a class of time delay systems. Systems & Control Letters, 55(7), 610–617.
• Kharitonov, V.L. (2012). Time-delay systems: Lyapunov functionals and matrices. Springer Science & Business Media.
• Neimark, J. (1949). D-subdivisions and spaces of quasipolynomials. Prikladnaya Matematika i Mekhanika, 13, 349–380.