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Course Description: Driven by recent technological advances and user specifications, most systems of today combine digital and analog devices, humans interacting with embedded computers, software distributed through networks, etc. As a result, they have state variables evolving both continuously and dis-continuously due to features such as events, logic… (More)

—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)

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)

Robust asymptotic stability for hybrid systems is considered. For this purpose, a generalized solution concept is developed. The first step is to characterize a hybrid time domain that permits an efficient description of the convergence of a sequence of solutions. Graph convergence is used. Then a generalized solution definition is given that leads to… (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)

— Two invariance principles for generalized hybrid systems are presented. One version involves the use of a nonincreasing function, like in the original work of LaSalle. The other version involves " meagreness " conditions. These principles characterize asymptotic convergence of bounded hybrid trajectories to weakly invariant sets. A detectability property… (More)

— We give an elementary proof of the fact that, for continuous-time systems, it is impossible to use (even discontinuous) pure state feedback to achieve robust global asymptotic stabilization of a disconnected set of points or robust global regulation to a target while avoiding an obstacle. Indeed, we show that arbitrarily small, piecewise constant… (More)

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Abstract—It is well known that controlling the attitude of a rigid body is subject to topological constraints. We illustrate, with examples, the problems that arise when using continuous and… (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)