2026/07/01 by Raffaele Iervolino, Sabato Manfredi, R. Ambrosino +1
Engineering · #Adaptive Control of Nonlinear Systems #Stability and Control of Uncertain Systems #Stability and Controllability of Differential Equations
paper · doi:10.1016/j.ejcon.2026.101579
openalex publication_date 2026/07/01 · openalex created_date 2026/07/24 · openalex updated_date 2026/07/29
This paper introduces the concept of Generalized Finite-Time Stability (GFTS) for discrete-time Linear Time-Varying (LTV) systems, extending the classical Finite-Time Stability (FTS) framework. Unlike traditional FTS, which mandates that the initial domain is a subset of the trajectory domain (both centered at the origin), GFTS allows for decoupled, off-origin initial and target domains, featuring a two-stage temporal definition: a reach phase from an initial set X 0 at k 0 to a terminal set X ¯ at k 1 , followed by a hold phase where the state remains in X ¯ until and including k 2 . This decoupling is essential for applications where the terminal set X ¯ is a temporary goal region that is not necessarily positively invariant and may not contain the origin. By restricting the sets to ellipsoids, necessary and sufficient conditions for GFTS are derived in terms of a set of Linear Matrix Inequalities (LMIs) based on forward and backward reachability analysis. Furthermore, the analysis of Generalized Finite-Time Stabilizability via linear state-feedback is developed, providing a computationally tractable solution using convex relaxations.