A note on static output-feedback for affine nonlinear systems (original) (raw)
On stabilization of nonlinear systems affine in control
2008 American Control Conference, 2008
In a recent paper, we developed a structural decomposition for MIMO nonlinear systems that are affine in control but otherwise general. In this paper we exploit the properties of such a decomposition for the purpose of solving the stabilization problem. In particular, this decomposition simplifies the conventional backstepping design, motivates a new backstepping design procedure that is able to stabilize some systems on which the conventional backstepping is not applicable, and allows the stabilization of non-square systems.
A hamilton-jacobi setup for the static output feedback stabilization of nonlinear systems
2002
The (local) static output feedback stabilization problem for a class of nonlinear (affine) systems is discussed. A sufficient condition is established and a (partial) converse is worked out. This condition provides a counterpart to a well-known result of linear systems theory. The effectiveness of the developed theory is illustrated with a simple example.
Output stabilization of square nonlinear systems
Automatica, 1997
This paper considers the problem of designing static-state feedback laws for output regulation of square affine nonlinear systems. The approach taken is to use input-output decoupling techniques to simplify the output regulation task into separate single-input single-output regulation tasks. In the case where the input-output decoupling matrix is full-rank, this approach yields the well-known input-output linearizing feedback law. In the case where the input-output decoupling matrix is rankdegenerate, it is shown that a static-state control law for output regulation can be constructed as long as the system can be input-output decoupled via dynamic feedback. The internal stability of the closed-loop system obtained using this approach is analysed. 01997 Elsevier Science Ltd.
Remarks on the Feedback Stabilization of System Affine in Control
European Journal of Control, 2001
manifolds theorem have been used by many authors for the construction of the stabilizing feedback law (see for instance and references therein). This paper is concerned with the stabilization of infinite dimensional systems described by the following abstract differential equation
2016
This paper presents some analyses about the robust practical stability of a class of nonlinear affine systems in the presence of non-vanishing perturbations based on the passivity concept. The given analyses confirm the robust passivity property of the perturbed nonlinear systems in a certain region. Moreover, robust control laws are designed to guarantee the practical stability of the perturbed systems. For this purpose, the control laws are designed in two cases. In the first case, it is assumed that the designer has freedom in choosing the outputs. In the second case, it is assumed that the outputs are predefined. In this case, first it is considered that the nominal system is passive between its inputs and outputs and then the control law is designed as static output feedback law for the perturbed system. Moreover, in the case that the nominal system is not passive, first, a law is designed such that the new nominal system is passive between the virtual inputs and the outputs. Then, the virtual input is designed as a static output feedback law such that the proposed controllers guarantee the practical stability of the perturbed system. Finally, the computer simulations are performed to show the efficacy and applicability of the designed controllers.
On the Synthesis of a Novel Nonlinear Feedback Control for Nonlinear Input-Affine Systems
2009 International Conference on Computational Intelligence, Modelling and Simulation, 2009
In this paper, we have developed a new approach to determine a feedback control law of a nonlinear input affine system by the use of efficient mathematical tools: the Kronecker product, the non-redundant state formulation and the polynomial representation of the transformation to a reference linear model, as well as a polynomial form of the control law. This method consists, as first step, in determining a polynomial transformation of coordinates to an equivalent linear model. Then, the synthesis of an analytic feedback control law via this nonlinear transformation has been presented in the second method step. The advantage of the proposed approach is the convenience of its implementation, as it copes with the complex differential geometric formalism of the exact linearization feedback control. To illustrate the efficiency of the presented approach, we have been applied it to a second order nonlinear model whose simulations results are presented.
On Controllability of Some Classes of Affine Nonlinear Systems
In this paper, we will present some recent progress in both global controllability and global asymptotical controllability of affine nonlinear systems. Our method is based on some basic facts in planar topology and in the geometric theory of ordinary differential equations. We will first present a necessary and sufficient condition for global controllability of general planar affine nonlinear systems, and then will give its generalizations to some high dimensional systems. Asymptotical controllability results will also be discussed and necessary and sufficient conditions will also be presented. Finally, we will show that the new controllability criterion can be easily applied to a number of practical examples.
Simultaneous stabilization via static output feedback and state feedback
IEEE Transactions on Automatic Control, 1999
In this paper, the simultaneous stabilization problem is considered using the matrix inequality approach. Some necessary and sufficient conditions for simultaneous stabilizability of r r r strictly proper multi-input/multi-output (MIMO) plants via static output feedback and state feedback are obtained in the form of coupled ARI's. It is shown that any such stabilizing feedback gain is the solution of some coupled linear quadratic control problems where every cost functional has a suitable cross term. A heuristic iterative algorithm based on the linear matrix inequality (LMI) technique is presented to solve the coupled matrix inequalities. The effectiveness of the approach is illustrated by numerical examples.