First-Moment Stability of Continuous-Time Markov Jump Linear Systems With Stationary, Time-Varying, and Polytopic Transition Rates

• 成果类型: Article
• 署名作者: De Iuliis, Vittorio; Manes, Costanzo
• 署名单位: Vita-Salute San Raffaele University; University of L'Aquila
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3640525
• 发表日期: 2026
• 关键词: stochastic stability; stabilization; sure

摘要

This work studies 1-moment stability for continuous-time Markov jump linear systems under both stationary and time-varying transition rates. For stationary transition rates, we propose novel sufficient stability conditions that are stated in terms of linear programs. These conditions offer a less restrictive and computationally simpler stability characterization compared to the commonly used mean-square stability analysis. Moreover, they offer a simple approach to also investigate the weaker notion of almost sure stability, which is implied by 1-moment stability. For the more general case of time-varying transition rates, we also propose 1-moment stability conditions expressed as linear inequalities. These conditions are derived by appropriately extending recent results on positive time-varying systems to general (i.e., not necessarily positive) systems. However, in the general case of time-varying transition rates without any particular structure, the conditions require infinitely many tests. Therefore, we explore finitely testable scenarios in which the transition rate matrix takes values within a polytope, as well as other relaxations.