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- Ricardo G. Sanfelice, Rafal Goebel, Andrew R. Teel
- IEEE Trans. Automat. Contr.
- 2007

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)

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)

- Christopher G. Mayhew, Ricardo G. Sanfelice, Andrew R. Teel
- IEEE Trans. Automat. Contr.
- 2011

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 (memoryless) discontinuous quaternion-based state-feedback control laws for global attitude stabilization. We propose a quaternion-based hybrid feedback scheme that solves the… (More)

- Rafal Goebel, Ricardo G. Sanfelice, Andrew R. Teel
- Systems & Control Letters
- 2008

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)

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 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)

This paper deals with the estimation of the state of linear time invariant systems for which measurements of the output are available sporadically. An observer with jumps triggered by the arrival of such measurements is proposed and studied in a hybrid systems framework. The resulting system is written in estimation error coordinates and augmented with a… (More)

- Ricardo G. Sanfelice, Andrew R. Teel
- Automatica
- 2011

A stability result is given for hybrid control systems singularly perturbed by fast but continuous actuators. If a hybrid control system has a compact set globally asymptotically stable when the actuator dynamics are omitted, or equivalently, are infinitely fast, then the same compact set is semiglobally practically asymptotically stable in the finite speed… (More)

- Yuchun Li, Ricardo G. Sanfelice
- CDC
- 2013

Motivated by the design of observers with good performance and robustness to measurement noise, the problem of estimating the state of a linear time-invariant system in finite time and with robustness to a class of measurement noise is considered. Using a hybrid systems framework, a hybrid observer producing an estimate that converges to the plant state in… (More)