Two Classes of Exponentially Stabilizable LPV Systems

Linear parameter-varying (LPV) systems, which have dynamics that vary according to a scheduling parameter, are capable of representing a wide variety of nonlinear and time-varying dynamics. The LPV paradigm preserves well-understood linear design methods, although the stability analysis of these systems has remained difficult. In a recent paper, it is shown that under some stringent conditions, a linear continuous-time gain-scheduled output feedback controller can be designed to provide closed-loop exponential stability; however, the conditions are hard to check, few examples are provided and all of the examples are stable. The goal of this article is to construct two large families of single-input single-output second-order systems, which satisfy these constraints while admitting wide ranges of parameter variation. The classes constructed include unstable and nonminimum phase systems, and consequently, this work facilitates the design of exponentially stabilizing LPV controllers for systems that are difficult to control.