Authors:
Elias August
1
;
Sigurdur Hafstein
2
;
Jacopo Piccini
1
;
Stefania Andersen
2
and
Anna Bavarsad
1
Affiliations:
1
Reykjavik University, Department of Engineering, Menntavegur 1, 102 Reykjavik, Iceland
;
2
University of Iceland, Faculty of Physical Sciences, Dunhagi 5, 107 Reykjavik, Iceland
Keyword(s):
Schur Complement, Sum of Squared Polynomials, Stochastic Differential Equation, Lyapunov Function, Gain Matrix, Numerical Method.
Abstract:
In this paper, we use the Schur Complement in combination with the sum of squares decomposition, first, to determine whether a nonlinear stochastic dynamical systems has a stable equilibrium and, second, to find a stabilising gain matrix for nonlinear dynamical systems. In both cases, we consider systems whose dynamics can be described using polynomial vector fields. Using many different examples, we highlight the effectivity of using our approaches. In some cases, we manage to obtain results that surpass previous ones. We believe that the presented approaches have many potential applications, for example, in the fields of aerospace and quantum control.