L 2 controller synthesis with L ∞ - bounded closed - loop impulse response

This article maybe used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. L z controller synthesis with Loo·bounded closed-loop impulse response Y. WILLIAM WANGt and DENNIS S. BERNSTEINt In this paper we consider an L 2 control problem with an L~ norm on the closed-loop impulse response. To do this we first construct an upper bound for the L~ norm of the impulse response of the closed-loop system. To perform controller synthesis, we then modify the standard LQG cost functional by including an additional penalty term that weights the L~ norm of the impulse response of the closed-loop system. A numerical example is given to illustrate the improved L~ response of the closed-loop system. Notation <!ft, C(6 real numbers, complex numbers spec (A) the set of eigenvalues of A P(A) spectral radius of A, max {IAI : AE spec (A)} amax(A), amin(A) maximum, minimum singular value of A az(A) second largest singular value of A a(A) spectral abscissa of A, max {ReA: AE spec(A)} IIAIIF,llx(t)llz Frobenius norm of A, (x T(t)x(t»l/2