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.
Retrieved from the University of Minnesota Digital Conservancy,
Content distributed via the University of Minnesota's Digital Conservancy may be subject to additional license and use restrictions applied by the depositor.