2016 Volume 9 Issue 4 Pages 165-172
In this paper, we study H∞ performance limitation analysis for continuous-time SISO systems using LMIs. By starting from an LMI that characterizes a necessary and sufficient condition for the existence of desired controllers achieving a prescribed H∞ performance level, we represent lower bounds of the best H∞ performance achievable by any LTI controller in terms of the unstable zeros and the unstable poles of a given plant. The transfer functions to be investigated include the sensitivity function (1+PK)-1, the complementary sensitivity function (1+PK)-1PK, and (1+PK)-1P, the first and the second of which are well investigated in the literature. As a main result, we derive lower bounds of the best achievable H∞ performance with respect to (1+PK)-1P assuming that the plant has unstable zeros. More precisely, we characterize a lower bound in closed-form by means of the first non-zero coefficient of the Taylor expansion of the plant P(s) around its unstable zero.