# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Stability regions of nonlinear dynamical systems: A constructive methodology. (English) Zbl 0689.93046
Summary: A constructive methodology for estimating stability regions of nonlinear dynamical systems is developed. The constructive methodology starts with a given Lyapunov function (either a global Lyapunov function or a local Lyapunov function) and yields a sequence of Lyapunov functions which are then used to estimate the stability region. The resulting sequence of estimated stability regions is shown to be a strictly monotonic increasing sequence and yet each of them remains inside the entire stability region. The significance of this methodology includes: 1) its ability to significantly reduce the conservativeness in estimating the stability regions; 2) its computational efficiency; 3) its adaptability; and 4) its sound theoretical basis. Furthermore, the methodology is applicable to estimate the stability regions of general nonlinear dynamical systems.
##### MSC:
 93D05 Lyapunov and other classical stabilities of control systems 93C10 Nonlinear control systems 34D20 Stability of ODE
##### Keywords:
stability regions