Abstract-The robustness properties of integral sliding-mode controllers are studied. This note shows how to select the projection matrix in such a way that the euclidean norm of the resulting perturbation is minimal. It is also shown that when the minimum is attained, the resulting perturbation is not amplified. This selection is particularly useful if integral sliding-mode control is to be combined with other methods to further robustify against unmatched perturbations.is taken as a special case. Simulations support the general analysis and show the effectiveness of this particular combination. Index Terms-, robust control, sliding-mode control (SMC), variable structure systems.

Abstract-The dynamics of many physical processes can be suitably described by Port-Hamiltonian (PH) models, where the importance of the energy function, the interconnection pattern and the dissipation of the system is underscored. To regulate the behavior of PH systems it is natural to adopt a Passivity-Based Control (PBC) perspective, where the control objectives are achieved shaping the energy function and adding dissipation. In this paper we consider the PBC techniques of Control by Interconnection () and Standard PBC. In the controller is another PH system connected to the plant (through a power-preserving interconnection) to add up their energy functions, while in Standard PBC energy shaping is achieved via static state feedback. In spite of the conceptual appeal of formulating the control problem as the interaction of dynamical systems, the current version of imposes a severe restriction on the plant dissipation structure that stymies its practical application. On the other hand, Standard PBC, which is usually derived from a uninspiring and non-intuitive "passive output generation" viewpoint, is one of the most successful controller design techniques. The main objectives of this paper are: (1) To extend the method to make it more widely applicable-in particular, to overcome the aforementioned dissipation obstacle. (2) To show that various popular variants of Standard PBC can be derived proceeding from a unified perspective. (3) To establish the connections between and Standard PBC proving that the latter is obtained restricting the former to a suitable subset-providing a nice geometric interpretation to Standard PBC-and comparing the size of the set of PH plants for which they are applicable.

We consider the problem of designing an integral sliding mode controller to reduce the disturbance terms that act on nonlinear systems with state-dependent drift and input matrix. The general case of both, matched and unmatched disturbances affecting the system is addressed. It is proved that the definition of a suitable sliding manifold and the generation of sliding modes upon it guarantees the minimization of the effect of the disturbance terms, which takes place when the matched disturbances are completely rejected and the unmatched ones are not amplified. A simulation of the proposed technique, applied to a dynamically feedback linearized unicycle, illustrates its effectiveness, even in presence of nonholonomic constraints.

It is well known that if the linear time invariant systemẋ = Ax + Bu, y = Cx is passive the associated incremental systemẋ = Ax + Bũ,ỹ = Cx, with(·) = (·) − (·) ⋆ , u ⋆ , y ⋆ the constant input and output associated to an equilibrium state x ⋆ , is also passive. In this paper, we identify a class of nonlinear passive systems of the formẋ = f (x) + gu, y = h(x) whose incremental model is also passive. Using this result we then prove that a large class of nonlinear RLC circuits with strictly convex electric and magnetic energy functions and passive resistors with monotonic characteristic functions are globally stabilizable with linear PI control.