Stability of switched systems with switching delay : application to remote operation of aircraft under distributed control

Unmanned aerial vehicles are becoming more and more useful tools for not nly the military, but law enforcement, search and rescue and scientific data colle ction. With the advent of inexpensive and reliable wireless communication, remote op erators are now able to control fleets of UAVs cooperating towards the acco mplishment of their tasks. As the complexity and size of these fleets increase, distrib uted control methods are needed – large fleet sizes will lead to intractable centra lized problems. Furthermore, UAVs, like most aircraft, are inherently hybrid sy stems, combining both discrete and continuous dynamics. This thesis attempts to combine hybrid and distributed control theories in a way useful for the operation o f UAVs, while taking communication delays inherent to a remote operator into account. Specifically, we consider the stability of block upper-triangular switched line ar systems with switching delay, when switching between stable modes. We show that the problem of proving globally uniformly asymptotic stability (GUAS) of a block upper-triangular switched linear system can be reduced to proving GUAS for each of its block diagonal subsystems. This allows for a scalable LMIbased computational test for GUAS under arbitrary switching whose complexity dep ends linearly on the number of block diagonal elements of the system. In cases for which the system is not GUAS under arbitrary switching, we partition the state space into regions in which switching will preserve GUAS despite a delay betw een the state measurements and switching time. This is accomplished by adding a delay buffer to standard Piecewise Lyapunov based partitions. Additiona lly, we show that the effect of the delay buffer on the standard Piecewise Lyap unov based partitions asymptotically approaches zero. Although we tailor these results to b ock upper-triangular switched linear systems, they are applicable to any switche d linear

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