Lyapunov Equations, Energy Functionals, and Model Order Reduction of Bilinear and Stochastic Systems
SIAM Journal on Control and Optimization
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This paper investigates the problem of model reduction based on balancing for uncertain discrete-time systems with multiplicative noise. Such systems can be considered as linear systems with both deterministic and stochastic uncertainties. Two linear matrix inequalities (LMIs) are proposed to find the balancing transformation, through which the original uncertain model with multiplicative noise is balanced. The reduced order model with the same structure as that of the original one is obtained by truncating the balanced model. An upper bound of the model reduction error is guaranteed. Based on the derived model reduction error bound, an optimization problem is suggested so that the solutions of the LMIs can be uniquely found and the model reduction error is ensured to be small.