Stability analysis of linear systems with multiple time-varying delays via a region partitioning approach and reciprocally convex combination lemmas. (English) Zbl 07900557
Summary: The delays-dependent stability analysis of linear systems with multiple time-varying delays is addressed in this study. To estimate the integral term that results from the differentiation of Lyapunov-Krasovskii functional (LKF), an improved region partitioning approach and relaxed lemmas are proposed. Based on all the delayed state information, the maximum delay interval \([-h,0]\) is separated into \(2N\) non-overlapping subintervals. Secondly, two novel generalized reciprocally convex combination lemmas (GRCCLs) are proposed, with Bessel-Legendre-based inequality, to estimate the integral terms generated by the region partitioning approach to obtain less conservative stability criteria. Finally, the obtained stability criteria is applied to simple linear systems and load frequency control (LFC) scheme of the two-area power system for stability analysis, and the effectiveness of proposed method is verified.
MSC:
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 93C05 | Linear systems in control theory |
| 93C43 | Delay control/observation systems |
Keywords:
multiple time-varying delays; stability analysis; region partitioning approach; generalized reciprocally convex combination lemmasReferences:
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