Control under Stochastic Multiplicative Uncertainties : Part II, Optimal Design for Performance

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Original languageEnglish
Article number7501589
Pages (from-to)1285-1300
Journal / PublicationIEEE Transactions on Automatic Control
Issue number3
Publication statusPublished - Mar 2017


This paper studies the optimal control design problem for linear discrete-time systems with stochastic multiplicative uncertainties. These uncertainties are assumed to be present in the control inputs and modeled as independent and identically distributed (i.i.d.) random processes. The optimal performance under study is defined in the mean-square sense, referred to as the mean-square optimal H2 performance. It is shown that the mean-square optimal H2 control problem via state feedback can be solved using a mean-square stabilizing solution to a modified algebraic Riccati equation (MARE). A necessary and sufficient condition for the existence of this solution is presented, which constitutes a generalization of the solution to the classic optimal H2 state feedback design problem, whereas the latter can be obtained by solving an algebraic Riccati equation (ARE). It is also proven that the optimal control design problem can be cast as an eigenvalue problem (EVP). For the output feedback case with possible input delays, we show that the mean-square optimal H2 control problem also amounts to solving an MARE, when the plant has no nonminimum phase zeros from the inputs to the measurement outputs. That is, the global optimal solution is obtained by solving an MARE incorporating the delays. The implication is that in this case a separation principle still holds.

Research Area(s)

  • AlgebraicRiccati equation, optimal control, output feedback, stochastic multiplicative uncertainties