Feedback stabilization of a second-order system: A nonmodal approach. (English) Zbl 0778.65047
The authors propose two nonmodal algorithms for feedback stabilization of a second-order, linear time-invariant system. The first algorithm requires no knowledge of eigenvalues and eigenvectors, its computational requirements are (1) the solution of a symmetric positive definite linear system and (2) the inversion of a small matrix. A remarkable feature of this algorithm is that it does not require knowledge of the stiffness matrix \(K\) and the damping matrix \(D\) at all for its implementation, making the algorithm feasible for practical use.
The second algorithm requires an estimate of a nonnegative number \(\sigma\), called the stability index, such that \(A+\sigma I\) is positively stable. These minimal computational requirements make the proposed algorithms suitable for practical implementations, even for large and sparse systems, using the state-of-the-art technique of matrix computations.
The second algorithm requires an estimate of a nonnegative number \(\sigma\), called the stability index, such that \(A+\sigma I\) is positively stable. These minimal computational requirements make the proposed algorithms suitable for practical implementations, even for large and sparse systems, using the state-of-the-art technique of matrix computations.
Reviewer: Yu Wenhuan (Tianjin)
MSC:
| 65K10 | Numerical optimization and variational techniques |
| 93C99 | Model systems in control theory |
| 93D15 | Stabilization of systems by feedback |
Keywords:
second-order linear system; nonmodal algorithms; feedback stabilization; linear time-invariant system; eigenvalues; eigenvectors; stiffness matrix; stability index; time-invariantReferences:
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