Uniform stabilization for linear systems with persistency of excitation.\n The neutrally stable and the double integrator cases

2007/02/23 by Antoine Chaillet, Yacine Chitour, Chaillet, Antoine +5 · 1 citation
Engineering · #Advanced Control Systems Optimization #Control and Stability of Dynamical Systems #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.math/0702687

openalex publication_date 2007/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider the controlled system dx/dt = Ax + \α(t)Bu where the pair\n(A,B) is stabilizable and \α(t) takes values in [0,1] and is\npersistently exciting, i.e., there exist two positive constants \μ,T such\nthat, for every t\≥ 0, \∫_t^t+T\α(s)ds\≥ \μ. In particular,\nwhen \α(t) becomes zero the system dynamics switches to an uncontrollable\nsystem. In this paper, we address the following question: is it possible to\nfind a linear time-invariant state-feedback u=Kx, with K only depending on\n(A,B) and possibly on \μ,T, which globally asymptotically stabilizes the\nsystem? We give a positive answer to this question for two cases: when A is\nneutrally stable and when the system is the double integrator.\n

Citations

• Stability Criteria for Switched and Hybrid Systems
• Multiple Lyapunov functions and other analysis tools for switched and hybrid systems

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