ISSN:
1573-2878
Keywords:
Nonzero sum linear-quadratic games
;
Nash strategies
;
coupled Riccati equations
;
Brower's fixed-point theorem
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The existence of linear Nash strategies for the linear-quadratic game is considered. The solvability of the coupled Riccati matrix equations and the stability of the closed-loop matrix are investigated by using Brower's fixed-point theorem. The conditions derived state that the linear closed-loop Nash strategies exist, if the open loop matrixA has a sufficient degree of stability which is determined in terms of the norms of the weighting matrices. WhenA is not necessarily stable, sufficient conditions for existence are given in terms of the solutions of auxiliary problems using the same procedure.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00933600
