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Register a new userFrequency criteria for exponential stability
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Oran Gannot
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We discuss some frequency-domain criteria for the exponential stability of nonlinear feedback systems based on dissipativity theory. Applications are given to convergence rates for certain perturbations of the damped harmonic oscillator.
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In this paper we deal with infinite-dimensional nonlinear forward complete dynamical systems which are subject to external disturbances. We first extend the well-known Datko lemma to the framework of the considered class of systems. Thanks to this generalization, we provide characterizations of the uniform (with respect to disturbances) local, semi-global, and global exponential stability, through the existence of coercive and non-coercive Lyapunov functionals. The importance of the obtained results is underlined through some applications concerning 1) exponential stability of nonlinear retarded systems with piecewise constant delays, 2) exponential stability preservation under sampling for semilinear control switching systems, and 3) the link between input-to-state stability and exponential stability of semilinear switching systems.
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We prove some criteria for uniform K-stability of log Fano pairs. In particular, we show that uniform K-stability is equivalent to $beta$-invariant having a positive lower bound. Then we study the relation between optimal destabilization conjecture and the conjectural equivalence between uniform K-stability and K-stability in the twisted setting.
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