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Mean-square small gain theorem for stochastic control: discrete-time case

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2 Author(s)
Jianbo Lu ; Ford Motor Co., Dearborn, MI, USA ; Skelton, R.E.

This paper 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 H2 norms of the involved transfer functions. Both robust stability and performance conditions are characterized by the new small-gain theorem

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Automatic Control, IEEE Transactions on  (Volume:47 ,  Issue: 3 )