### A Leighton-Borůvka formula for Morse conjugate points

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In this paper, the finite-time stabilization problem of chained form systems with parametric uncertainties is investigated. A novel switching control strategy is proposed for adaptive finite-time control design with the help of Lyapunov-based method and time-rescaling technique. With the proposed control law, the uncertain closed-loop system under consideration is finite-time stable within a given settling time. An illustrative example is also given to show the effectiveness of the proposed controller....

This paper deals with integrability issues of the Euler-Lagrange equations associated to a variational problem, where the energy function depends on acceleration and drag. Although the motivation came from applications to path planning of underwater robot manipulators, the approach is rather theoretical and the main difficulties result from the fact that the power needed to push an object through a fluid increases as the cube of its speed.

The use of a multi-input control design procedure for uncertain nonlinear systems expressible in multi-input parametric-pure feedback form to determine the control law for a class of mechanical systems is described in this paper. The proposed procedure, based on the well-known backstepping design technique, relies on the possibility of extending to multi-input uncertain systems a second order sliding mode control approach recently developed, thus reducing the computational load, as well as increasing...

A generalized structure of complementary matrices involved in the input-state- output Inclusion Principle for linear time-invariant systems (LTI) including contractibility conditions for static state feedback controllers is well known. In this paper, it is shown how to further extend this structure in a systematic way when considering contractibility of dynamic controllers. Necessary and sufficient conditions for contractibility are proved in terms of both unstructured and block structured complementary...

The paper is divided in two parts. In the first part a deep investigation is made on some system theoretical aspects of periodic systems and control, including the notions of ${H}_{2}$ and ${H}_{\infty}$ norms, the parametrization of stabilizing controllers, and the existence of periodic solutions to Riccati differential equations and/or inequalities. All these aspects are useful in the second part, where some parametrization and control problems in ${H}_{2}$ and ${H}_{\infty}$ are introduced and solved.

We consider the stabilization of a rotating temperature pulse traveling in a continuous asymptotic model of many connected chemical reactors organized in a loop with continuously switching the feed point synchronously with the motion of the pulse solution. We use the switch velocity as control parameter and design it to follow the pulse: the switch velocity is updated at every step on-line using the discrepancy between the temperature at the front...

In the paper, we unify and extend some basic properties for linear control systems as they appear in the continuous and discrete cases. In particular, we examine controllability, reachability, and observability for time-invariant systems and establish a duality principle.