## What is Polytopic uncertainty?

Polytopic uncertainty is found in the inertia matrix because this type of parameter is difficult to obtain for a real application. Inertia matrix polytopic uncertainty consists in the determination of the selected inertia matrix, the time-variable uncertainty, and its respective vertices.

What is Polytopic system?

Polytopic representation is one of the most general ways to describe without any conservatism physical parameter uncertainty. In this representation, the uncertain system belongs to a polytope which is the convex hull of the parameters of a set of models (vertices).

### What is polytopic uncertainty?

In this representation, the uncertain system belongs to a polytope which is the convex hull of the parameters of a set of models (vertices). Polytopic uncertainty can cover the well-known interval and linear parameter uncertainty as well as multi-model structures.

What is polytopic representation?

Polytopic representation is one of the most general ways to describe without any conservatism physical parameter uncertainty. In this representation, the uncertain system belongs to a polytope which is the convex hull of the parameters of a set of models (vertices).

#### How to analyze the stability of polytopic systems?

Robust stability of polytopic systems is analyzed either in the polynomial form using the generalized Kharitonov theorem ( Bhattacharyya, Chapellat, & Keel, 1995) or in the state space using the concept of quadratic stability. In the latter, a Lyapunov function should be found for all vertices of the polytopic system.

Can we decide the stability of uncertain linear systems?

We survey the problem of deciding the stability or stabilizability of uncertain linear systems whose region of uncertainty is a polytope. This natural setting has applications in many fields of applied science, from control theory to systems engineering to biology.