J. Hespanha, O. Yakimenko, I. Kaminer (USA), and A. Pascoal (Portugal)
nonlinear control, navigation, real-time systems,unmanned vehicles
This paper studies linear parametrically varying systems (LPVs) with brief instabilities. LPVs are ubiquitous because they provide an elegant, albeit conservative framework for the study of nonlinear systems. This is done by analyzing a related family of linear time-invariant systems parameterized by a parameter p that lives in some compact set. In the conventional set-up of LPV theory, it is usually required that the system matrices in the family of parameterized linear systems be stable for all values of p. However, there are interesting problems for which this requirement does not hold true, that is, the linear system matrices are unstable for some of values of the parameter p, instability occurring for brief instants of time only. This paper introduces the concept of LPVs with brief instabilities and derives tools for stability and performance analysis of these systems, where performance is evaluated in terms of L2 induced norms. The main results show that stability and performance can be assessed by examining the feasibility of parameterized sets of Linear Matrix Inequalities (LMIs). An application to the problem is the design of nonlinear vision/inertial navigation filter for an aircraft approaching an aircraft carrier [1]. The results developed pro vide the proper framework to deal with out-of-frame events that arise when the vision system loses its target temporarily.
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