IEEE Transactions on Automatic Control, Vol.47, No.3, 490-494, 2002
Mean-square small gain theorem for stochastic control: Discrete-time case
This note presents a small gain theorem in the mean square sense for multiple (interconnected) linear systems with multiplicative noises. The small-gain theorem is proposed in terms of the spectral radius of a matrix, whose elements are the squares of H-2 norms of the involved transfer functions. Both robust stability and performance conditions are characterized by the new small-gain theorem.
Keywords:internal mean square stability (IMSS);multiplicative noise uncertainty;robust control;stochastic control