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Many dynamical systems that occur naturally in the description of physical processes are piecewise-smooth (PWS). That is, their motion is characterized by periods of smooth evolutions interrupted by instantaneous events, such as impact, switching, sliding and other discrete state transitions. These phenomena arise in any application involving friction, collision, intermittently constrained systems or processes with switching components. For example, in mechanical systems with impacts and friction, power converters with switching elements, gene regulatory networks, and many others.
Discontinuities are also designed intentionally in regulation and stabilization problems, not only as an alternative to classical smooth control but also because many control systems cannot be stabilized by continuous state-dependent feedback. Examples of discontinuous control range from relay control to sliding mode control, from switched control to hybrid control. We list below some of the specific research topics that are of our interest:
Analysis of discontinuity-induced bifurcation
Incremental and differential stability analysis
Synchronization in networks of PWS systems
Adaptive control of PWS systems
Switched control design
State observer design
Synchronization in networks of PWS systems
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