Stabilization of nonlinear systems by similarity transformations. (1998)

• Record Type: Journal Article
• Authors: Zuber, Irina E.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 11:Number 4(1998)
• Page Start: 519
• Page End: 526
• Publication Date: 1998
• Subjects: similarity transformation -- derivative in virtue of system -- stabilization; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953398000422
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : For a system x ˙ = A ( x ) + b ( x ) u, u ( x ) = s ∗ ( x ) x, x ∈ ℝ n, where the pair ( A ( x ), b ( x ) ) is given, we obtain the feedback vector s ( x ) to stabilize the corresponding closed loop system. For an arbitrarily chosen constant vector g, a sufficient condition of the existence and an explicit form of a similarity transformation T ( A ( x ), b ( x ), g ) is established. The latter transforms matrix A ( x ) into the Frobenius matrix, vector b ( x ) into g, and an unknown feedback vector s ( x ) into the first unit vector. The boundaries of A ˜ ( y, g ) are determined by the boundaries of { ∂ k A ( x ) ∂ x k, ∂ k b ( x ) ∂ x k }, k = 0, n − 1 ¯ . The stabilization of the transformed system is subject to the choice of the constant vector g .