Sufficient Conditions For Robust Stabilizability Research Articles

Stabilization of uncertain systems in the presence of finite data-rate feedback

In this paper, we address the stabilizability of uncertain systems in the presence of finite data-rate feedback. In our formulation, a finite data-rate link is used to transmit state measurements between the plant and the controller. We determine sufficient conditions for internal and external stabilizability of the feedback loop. Stability in the presence of uncertainty in the plant is analyzed using a small-gain argument. We show that larger uncertainty can be tolerated at the expense of higher transmission rates. A comparison is established between the sufficient conditions for robust stabilizability and the necessary conditions for the stability of the nominal model. We also suggest how our results can be used to determine the stabilizability of a class of non-linear systems.

The graph topology for linear plants with applications to nonlinear robust stabilization

The graph topology is defined for the set of finite-dimensional linear time-varying plants that are internally stabilizable by output feedback. This follows some earlier results of M. Vidyasagar et al. (1982) on time-invariant systems. Feedback connections of linear time-varying plants and general nonlinear time-varying controllers are considered, and it is shown that the graph topology is the weakest topology in which feedback stabilization is a robust property. Using this result, necessary and sufficient conditions for robust stabilizability of families of linear time-varying plants with parametric uncertainty are derived.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Robust stabilization of distributed systems

This paper is devoted to the problem of robust stabilization for a class of distributed plants. We consider the gain margin optimization problem and the robust stabilization problem for multiplicative perturbations. Using techniques from interpolation theory and complex variables, we obtain explicit necessary and sufficient conditions for robust stabilizability. A few examples are included to illustrate the results.

Robust stabilizability for a class of transfer functions

This paper is concerned with the robust stabilizability for single-input single-output plants. Robust stabilizability means that a fixed controller can stabilize simultaneously all the plants in a given class which is characterized by a frequency-dependent uncertainty band function around the transfer function of a nominal model. A necessary and sufficient condition for robust stabilizability is derived based on the well-known Nevanlinna-Pick theory in classical analysis. It is shown that the values of the uncertainty band function should be restricted within a certain range at the unstable poles of the nominal model, in order for the class to be robustly stabilizable. A procedure of synthesizing a robust stabilizer is given and the parametrization of all the robust stabilizers is also shown.