## 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.