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—The paper shows several versions of the (LaSalle's) invariance principle for general hybrid systems. The broad framework allows for nonuniqueness of solutions, Zeno behaviors , and does not insist on continuous dependence of solutions on initial conditions. Instead, only a mild structural property involving graphical convergence of solutions is posed. The(More)
— Recently, Linear Temporal Logic (LTL) has been employed as a tool for formal specification in dynamical control systems. With this formal approach, control systems can be designed to provably accomplish a large class of complex tasks specified via LTL. For this purpose, language generating Buchi automata with finite abstractions of dynamical systems have(More)
Invariance principles for hybrid systems are used to derive invariance principles for nonlinear switching systems with multiple Lyapunov-like functions. Dwell-time, persistent dwell-time, and weak dwell-time solutions are considered. Asymptotic stability results are deduced under further observability assumptions or common bounds on the Lyapunov-like(More)
— Global asymptotic stabilization of the attitude of a rigid body is hindered by major topological obstructions. In fact, this task is impossible to accomplish with continuous state feedback. Moreover, when the attitude is parametrized with unit quaternions, it becomes impossible to design a globally stabilizing state feedback (even discontinuous) that is(More)
We study how convergence of an observer whose state lives in a copy of the given system's space can be established using a Riemannian metric. We show that the existence of an observer guaranteeing the property that a Riemannian distance between system and observer solutions is nonincreasing implies that the Lie derivative of the Riemannian metric along the(More)
We derive optimality conditions for the paths of a Dubins vehicle when the state space is partitioned into two patches with different vehicle's forward velocity. We recast this problem as a hybrid optimal control problem and solve it using optimality principles for hybrid systems. Among the optimality conditions, we derive a " refraction " law at the(More)
material have the responsibility to inform all of the authors promptly if they wish to reuse, modify, correct, publish, or distribute any portion of this report. Abstract A mathematical model for a two-gene regulatory network is derived and several of their properties analyzed. Due to the presence of mixed continuous/discrete dynamics and hysteresis, we(More)
Motivated by applications of systems interacting with their environments, we study the design of passivity-based controllers for a class of hybrid systems in which the energy dissipation may only happen along either the continuous or the discrete dynamics. A general definition of passivity, encompassing the said special cases, is introduced and, along with(More)