- Negative-Imaginary Systems Mechanical structures with colocated force actuators and position sensors do not yield positive-real systems because the product of force and position is not equal to the power provided by the actuator. In this case, the transfer function matrix from the force actuator inputs $u_1(t),…,u_m()t$ to the position sensor outputs $y_1(t),…,y_m()t$ is of the formwhere, for all $i$,$k_i>0$,$\omega_i>0$, and $\psi_i$ is an mx1 vector.
- The Strict Bounded Real Lemma This article presents the strengthened version of the Bounded Real Lemma found in “A first principles solution to the non-singular $ H^{\infty} $ control Problem.”The result gives a strict $H^\infty$ norm bound for non-minimal realizations.