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In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation , for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature ...
In nonlinear control and stability theory, the Popov criterion is a stability criterion discovered by Vasile M. Popov for the absolute stability of a class of nonlinear systems whose nonlinearity must satisfy an open-sector condition.
In the mathematical field of model theory, a theory is called stable if it satisfies certain combinatorial restrictions on its complexity. Stable theories are rooted in the proof of Morley's categoricity theorem and were extensively studied as part of Saharon Shelah's classification theory, which showed a dichotomy that either the models of a theory admit a nice classification or the models ...
Some extensions of Liapunov's second method, IRE Transactions on Circuit Theory, CT-7, pp. 520–527, 1960. (PDF Archived 2019-04-30 at the Wayback Machine) Barbashin, E. A.; Nikolai N. Krasovskii (1952). Об устойчивости движения в целом [On the stability of motion as a whole]. Doklady Akademii Nauk SSSR (in Russian).
In the control system theory, the Routh–Hurwitz stability criterion is a mathematical test that is a necessary and sufficient condition for the stability of a linear time-invariant (LTI) dynamical system or control system. A stable system is one whose output signal is bounded; the position, velocity or energy do not increase to infinity as ...
Ideas of structural stability were taken up by Stephen Smale and his school in the 1960s in the context of hyperbolic dynamics. Earlier, Marston Morse and Hassler Whitney initiated and René Thom developed a parallel theory of stability for differentiable maps, which forms a key part of singularity theory. Thom envisaged applications of this ...
He created the modern theory of the stability of a dynamical system. In the theory of probability, he generalized the works of Chebyshev and Markov, and proved the Central Limit Theorem under more general conditions than his predecessors. The method of characteristic functions he used for the proof later found widespread use in probability ...
This is a technique used as a stability criterion in the field of classical control theory developed by Walter R. Evans which can determine stability of the system. The root locus plots the poles of the closed loop transfer function in the complex s-plane as a function of a gain parameter (see pole–zero plot).