This paper presents a variational approach to ℋ∞ control with transients in the state feedback case. The approach here provides a precise description with equality, instead of inequality, in the necessary and sufficient conditions for the existence of a linear controller. Furthermore, the solution existence and uniqueness are proved in terms of certain properties of the indefinite Riccati equations derived in this paper. The linear time-variant (LTV) plant on ﬁnite horizon is considered ﬁrst, and then the results are extended to the linear time-invariant (LTIV) plant on the inﬁnite horizon. By this approach, it can be directly concluded that only suboptimal ℋ∞ state feedback control can be achieved in an input–output point of view and that the performance measure γ(μ1/2 used in this paper) is a strict upper bound.
Lu, Wayne W.; Balas, Gary J.; Lee, E.B..
A Variational Approach to ℋ∞ Control with Transients.
Institute of Electrical and Electronic Engineers.
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