Motivated by applications of systems interacting with their environments, we study the design of passivity-based controllers for a class of hybrid systems in which the energy dissipation may only happen along either the continuous or the discrete dynamics. A general definition of passivity, encompassing the said special cases, is introduced and, along with detectability and solution conditions, linked to stability and asymptotic stability of compact sets. The proposed results allow us to take advantage of the passivity property of the system at flows or at jumps and are employed to design passivity-based controllers for the class of hybrid systems of interest. Two applications, one pertaining to a point mass physically interacting with a wall and another about controlling a ball bouncing on an actuated surface, illustrate the definitions and results throughout the paper. © 2013 Elsevier Ltd. All rights reserved.

Building from recent results on passivity for a class of hybrid systems, we investigate the properties of negative feedback interconnections of such systems. We establish links between the passivity properties of the individual subsystems and passivity, stability, and asymptotic stability of their interconnection. As a main difference to the continuous time counterpart, it is found that the sum of the two storage functions of two individual hybrid subsystems may not be a storage function for their interconnection. This issue motivates exploring additional sufficient conditions that guarantee that passivity and stability of the interconnected system hold using the individual storage functions. Throughout the paper, an application and examples illustrate the definitions and the results obtained. © 2014 American Automatic Control Council.

This work proposes a feedback control strategy capable of controlling the dynamics of an under-actuated Vertical Take-Off and Landing (VTOL) aerial vehicle to track a desired trajectory globally with respect to the initial conditions. The novelty of the proposed design is the idea of considering a cascade control paradigm in which the attitude dynamics, which are governed by means of a hybrid controller capable of overcoming the well-known topological constraints, and the position dynamics of the vehicle play respectively the role of the inner and of the outer loop. The stability properties of the proposed controller are then derived by analyzing the interconnection between a hybrid system, namely the closedloop attitude dynamics, and a continuous time system, given by the closed-loop position dynamics. The proposed algorithms are then demonstrated by means of simulations obtained considering a miniature quadrotor prototype. ©2013 IEEE.

This paper proposes a feedback control strategy to let the dynamics of a class of under-Actuated vertical take-off and landing (VTOL) aerial vehicle tracking a desired position and attitude trajectory globally with respect to the initial conditions. The proposed feedback controller is derived following an inner-outer loop control paradigm, namely by considering the attitude, which is governed by means of a hybrid controller so as to overcome the well-known topological constraints, serving as a virtual input to stabilize the aircraft position. Two different approaches, the first one obtained by assuming perfect knowledge of the vehicle dynamics and the second one obtained by considering uncertainties and exogenous disturbances, are proposed and compared by analyzing the interconnection between the hybrid attitude and the continuous-Time position closed-loop subsystems. The effectiveness of the obtained results is demonstrated by means of simulations and experiments using a miniature quadrotor prototype.