Robust decentralized controller with multi-objective performance design for stochastic large-scale systems via linear matrix inequalities approach

The present paper focuses on a class of stochastic large-scale interconnected systems with norm-bounded and time-varying parameter uncertainties. The problem addressed is the design of a robust decentralized controller such that the corresponding interconnected closed-loop system satisfies certain multi-objective performance requirements for all admissible uncertainties. The objectives of this robust design consist of individual state variance limitation, white noise attenuation constraints on H_∞ norm, and pole placement specification. Sufficient conditions, based on a quadratic Lyapunov function, for multi-objective robustness are derived in terms of linear matrix inequalities (LMIs). It is shown that the problem of multi-objective robust decentralized control can be solved and the effectiveness of the proposed approach is illustrated by a numerical example.