My research interests are focused on mathematical control theory, with special emphasis on stability analysis, optimal control and model reduction.
Discontinuous Phasor Transform.
I introduced a new “discontinuous phasor transform”. The classical phasor transform greatly simplifies the dynamic analysis of electrical devices because it changes integro-differential equations in more tractable algebraic equations. While the classical transform can be used only for sinusoidal sources, the new transform can be used for switching sources. In particular, the discontinuous phasor transform allows analysing the steady-state behaviour of discontinuous electronic devices in closed-form without approximations. The “I-V characteristics” for inductors, capacitors and resistors are described in terms of this new phasor transform. The new quantities maintain their physical meaning: instantaneous power, average power and reactive power are defined in the phasor domain. The phasor transform has been applied to the study of the steady-state response of power inverters and of wireless power transfer systems with non-ideal switches.
A working example of the discontinuous phasor transform can be downloaded from here.
A novel system theoretic approach for wireless power transfer systems with applications to implantable medical devices and consumer electronics
This project will study new dynamic power and frequency control strategies for making IPT systems adaptive to changes of the transmission and environmental conditions. The focus of the project is to develop a novel system theoretic approach derived by control theory techniques as opposed to the standard electrical/physical approach (which will nevertheless retain an important role).
Model order reduction
I studied the problem of model reduction by moment matching for linear and nonlinear time-delay systems, including neutral differential time-delay systems with discrete-delays and distributed delays. I also investigated the problem of characterizing the moments for "interpolation signals" which do not have an implicit model, i.e. they do not satisfy a differential equation. Particular attention is devoted to discontinuous signals for their practical applications. I proposed an algorithm for the estimation of the moments of linear systems and nonlinear (time-delay) systems from input/output data. I also worked on the problem of model reduction of singular systems and power systems.
Asymptotic properties of nonlinear systems
I worked on the analysis of the stability of large-scale systems proposing several theorems, inspired by the Krasovskii-LaSalle invariance principle, to establish "lim inf" convergence results. These properties are useful to describe the oscillatory behaviour of the solutions of dynamical systems. The theorems resemble "lim inf" Matrosov and Small-gain theorems, and they are based on a "lim inf" Barbalata's Lemma.