TY - GEN
T1 - Diagonal stability of stochastic systems subject to nonlinear disturbances and diagonal H2 norms
AU - Langbort, C.
AU - Ugrinovskii, V.
N1 - Funding Information:
This work was supported by the Australian Research Council grant DP0987369 to V.U., and, in part, by NSF grant CMMI 08-26469 to C.L. The material in this paper was partially presented at the 49th IEEE Conference on Decision and Control, December 15–17, 2010, Atlanta, Georgia, USA. This paper was recommended for publication in revised form by Associate Editor Tongwen Chen under the direction of Editor Ian R. Petersen.
PY - 2010
Y1 - 2010
N2 - A known result in the stability theory of stochastic systems with nonlinear Lipschitz-bounded noise intensity states that the robust stability radius of such a stochastic system is equal to the inverse of the H2 norm of its 'noise-to-output' transfer function. This paper extends this result to the case where one is interested in the diagonal stability of the system under consideration. This problem arises naturally when studying large-scale interconnected systems subject to random perturbations, as one is often interested in using diagonal or block-diagonal Lyapunov functions for such plants. The main result of the paper is the characterization of the diagonal stochastic stability radius, which is similar to the mentioned result for non-diagonal stability.
AB - A known result in the stability theory of stochastic systems with nonlinear Lipschitz-bounded noise intensity states that the robust stability radius of such a stochastic system is equal to the inverse of the H2 norm of its 'noise-to-output' transfer function. This paper extends this result to the case where one is interested in the diagonal stability of the system under consideration. This problem arises naturally when studying large-scale interconnected systems subject to random perturbations, as one is often interested in using diagonal or block-diagonal Lyapunov functions for such plants. The main result of the paper is the characterization of the diagonal stochastic stability radius, which is similar to the mentioned result for non-diagonal stability.
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U2 - 10.1109/CDC.2010.5718024
DO - 10.1109/CDC.2010.5718024
M3 - Conference contribution
AN - SCOPUS:79953146924
SN - 9781424477456
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 3188
EP - 3193
BT - 2010 49th IEEE Conference on Decision and Control, CDC 2010
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 49th IEEE Conference on Decision and Control, CDC 2010
Y2 - 15 December 2010 through 17 December 2010
ER -