Computation of zeros of linear multivariable systems

Robust decentralized control of HVAC systems using -performance measures

“…Then, as shown by Davison [5], a solution to the robust decentralized servomechanism problem for Condition (i) was verified by using the method developed by Patel and Misra [11]. As far as condition (ii) is concerned, computation of the transmission zeros of ðC; A; BÞ given by Emami-Naeini and Van Dooren [12] indicated that the system has no transmission zeros at the origin. Therefore, we conclude that a solution to the robust decentralized servomechanism problem for (3.3) exists.…”

Modelica Libraries for Linear Control Systems

“…However, this algorithm fails if the system has not the same number of inputs and outputs or if one of the matrices B or C does not have full column or full row rank respectively. For this reason, in the LinearSystems library the algorithm from [5] is used to calculate the invariant zeros of arbitrary StateSpace systems, i.e., with arbitrary numbers of inputs and outputs and rank deficient matrices. The approach is to compress the matrices (A, B, C, D) with QR-decompositions to (A r , B r , C r , D r ) such that a reduced order system matrix…”

A Study on LQG/LTR Control for Damping Inter-Area Oscillations in Power Systems

“…Table III illustrates the location of the transmission zeros for the Kalman filter compared to the open-loop transmission zeros of the squared/minimum-phase design system (minimum damping ratio assigned is 0.45). The Kalman gain vector is given by (31). Note that the poles in rows 1, 2, 3, and 5 approach the OL transmission zeros (defined to be minimum phase and well-damped), while the remaining poles in rows 4, 6, and 7 ultimately will move towards as (from optimal root loci as discussed earlier) (31)…”