Exponential Decay Rate of Linear Port-Hamiltonian Systems: A Multiplier Approach

• 成果类型: Article
• 署名作者: Mora, Luis A.; Morris, Kirsten
• 署名单位: University of Waterloo
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3332008
• 发表日期: 2024
• 页码: 1767-1772
• 关键词: control theory; propagation; Stability criteria; system performance; Symmetric matrices; STANDARDS; Scattering parameters; Boundary dissipation; decay rate; distributed parameter systems (DPS); exponential stability; infinite-dimensional system; Partial differential equations; port-Hamiltonian systems (PHS)

摘要

In this work, the multiplier method is extended to obtain a general lower bound on the exponential decay rate for port-Hamiltonian systems in one space dimension with boundary dissipation. The physical parameters of the system may be spatially varying. It is shown that, under assumptions of boundary or internal dissipation, the system is exponentially stable. This is established through a Lyapunov function defined through a general multiplier function. Furthermore, an explicit bound on the decay rate in terms of the physical parameters is obtained. The method is applied to a number of examples.