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We extend the positive real balancing procedure for passive linear systems to the nonlinear systems case. We show that, just like in the linear case, model reduction based on this technique preserves passivity. [ABSTRACT FROM AUTHOR]

It is well known that energy balancing control is stymied by the presence of pervasive dissipation. To overcome this problem in electrical circuits, the authors recently proposed the alternative paradigm of power shaping—where, as suggested by its name, stabilization is achieved shaping a function akin to power instead of the energy function. In this paper we extend this technique to general nonlinear systems and apply it for the stabilization of the benchmark tunnel diode circuit. It is shown that, in contrast with other techniques recently reported in the literature, e.g. piecewise approximation of nonlinearities, power shaping yields a simple linear static state feedback that ensures (robust) global asymptotic stability of the desired equilibrium. [ABSTRACT FROM AUTHOR]

In the present work we are interested on the derivation of power-based passivity properties for a certain class of non-linear mechanical systems. While for general mechanical systems, it is of common use to adopt a storage function related to the system's energy in order to show passivity and stabilize the system on a desired equilibrium point (e.g., IDA-PBC [1]), we want here to obtain similar properties related to the system's power. The motivation arises from the idea that in some engineering applications (satellite orbit motion, aircraft dynamic, etc⋯) seems more sensible to cope with the power flowing into the system instead of the energy that, for stabilization purposes, means to consider the systems's equilibrium the state for which the energy flow-rate (i.e., system's power) achieve its minimum. In this respect, we recall first the power-based description for a certain class of (non)-linear mechanical systems given in [2] and then we give sufficient conditions to obtain power-based passivity properties, provided a suitable choice of port-variables. We conclude with the example of the inverted pendulum on the cart. [ABSTRACT FROM AUTHOR]