Stabilization of nonlinear systems: A bilinear approach

In this paper the Routh stability criterion [16] has been developed into control Routh array. Some formulas for calculating the array are provided. Certain properties are investigated. Using it, the problem of stabilization of bilinear systems via constant controls is solved. Then by converting the problems, the method of control Routh array is also used to solve some other stability related problems, such as the stabilization of control systems, the stability of uncertain Hurwitz matrix and the stability of interval matrices. Several algorithms have been developed to provide numerical solutions.

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“…We start with the stabilization of system (1) with constant controls. When n = 2 and m = 1 [7] provided necessary and sufficient conditions.…”

Section: Preliminarymentioning

confidence: 99%

Control Routh Array And Its Applications

Cheng

Tarn

2003

Asian Journal of Control

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“…In this case the conclusion used in the second part of the proof would not be possible. 5. Numerical calculation of the discrete feedback The numerical method proposed follows the ideas described in 14] which are based on a discretization scheme by I. Capuzzo Dolcetta, H. Ishii and M. Falcone 4], 11] and 3].…”

Section: (26)mentioning

confidence: 99%

Discrete feedback stabilization of semilinear control systems

Grüne¹

1996

ESAIM: COCV

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Abstract. F or continuous time semilinear control systems with constrained control values stabilizing discrete feedback c o n trols are discussed. It is shown that under an accessibility condition exponential discrete feedback stabilizability is equivalent to open loop exponential asymptotic null controllability. A n umerical algorithm for the computation of discrete feedback c o n trols is presented and a numerical example is discussed.

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“…Homogeneous bilinear systems (1) have the special feature that there may exist 'constant' stabilizing control inputs. Although stabilizing controllers for (both homogeneous and nonhomogeneous) bilinear systems have been extensively studied in the literature, they are chiefly quadratic or discontinuous functions of the state [4][5][6][7][8], and the problem of constructing constant stabilizing control inputs is not well studied in the context of bilinear systems theory, except for low-dimensional cases [9][10][11]. On the other hand, in the context of linear systems theory, the static output feedback stabilization problem or the decentralized/structured feedback stabilization problem, which is equivalent to the constant input stabilization problem of bilinear systems, has been extensively studied (see [12][13][14][15][16][17][18][19][20][21][22][23][24] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Stabilization of continuous‐time homogeneous bilinear systems by constant inputs through nonlinear minimization with applications to the static output feedback stabilization problem

Hanba

2007

Intl J Robust & Nonlinear

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SUMMARYAn algorithm to provide constant-input stabilizing control inputs for multi-input continuous-time bilinear systems is proposed in this paper. The algorithm is based on the formal discrete-time approximation of the system and the unconstrained nonlinear minimization. The key features of the new algorithm are as follows. First, the formal discrete-time approximation makes the set of stabilizing control inputs starshaped centred at the origin, hence the minimization is to be performed only in a neighbourhood of the origin selected by the designer. Second, the algorithm is always capable of finding a solution if one exists, as long as the minimization inside the neighbourhood is successful. Third, by a slight modification, the algorithm permits us to place all the eigenvalues of the system inside a rectangular region in the complex plane, as long as it is feasible. The algorithm is also applicable to the static output feedback stabilization problem of linear time-invariant systems.

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Stabilization of nonlinear systems: A bilinear approach

Cited by 29 publications

References 16 publications

Control Routh Array And Its Applications

Control Routh Array And Its Applications

Discrete feedback stabilization of semilinear control systems

Stabilization of continuous‐time homogeneous bilinear systems by constant inputs through nonlinear minimization with applications to the static output feedback stabilization problem

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