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Stabilization methods for nonlinear second-order systems

Skruch P.

Archives of Control Sciences

2009

Vol. 19, no. 2

205-216

The goal of this paper is to study stabilization techniques for a system described by nonlinear second-order differential equations. The problem is to determine the feedback control as a function of the state variables. It is shown that the following controllers can asymptotically stabilize the system: linear position feedback, linear velocity feedback and a group of nonlinear feedbacks. The asymptotic stability of the closed-loop system has been proved by LaSalle's invariance principle. The results of numerical computations are included to verify theoretical analysis and mathematical formulation.

Optimization and Pole Assignment in Control System Design

Chu E. K.

International Journal of Applied Mathematics and Computer Science

2001

Vol. 11, no 5

1035-1053

Some elementary optimization techniques, together with some not so well-known robustness measures and condition numbers, will be utilized in pole assignment. In particular, "Method 0" by Kautsky et al. (1985) for optimal selection of vectors is shown to be convergent to a local minimum, with respect to the condition number 1/2 ||X||_F^2 - ln |det X|. This contrasts with the misconception by Kautsky et al. that the method diverges, or the recent discovery by Yang and Tits (1995) that the method converges to stationary points.