For the purpose of studying stability of hybrid automata, we will again drop reference to inputs (and outputs) of the system and focus on the state trajectory. Later, we will bring the inputs (and outputs) back in when we talk about stabilizing controllers. For reference to the following material, see [1, 2], Chapters 3 and 2 respectively.

Hybrid automata provide a language for modeling and analyzing digital and analogue computations in real-time systems. Hybrid automata are studied here from a dynamical systems perspective. Necessary and sufficient conditions for existence and uniqueness of solutions are derived and a class of hybrid automata whose solutions depend continuously on the initial state is characterized. The results ...

Timed and weak timed simulation relations are often used to show that operations on hybrid systems result in equivalent behavior or in conservative overapproximations. Given that systems are frequently designed and verified in a modular approach, it is desirable that this relationship is compositional, which is not the case for hybrid systems in general. We identify subclasses of linear hybrid ...

Template polyhedra generalize intervals and octagons to polyhedra whose facets are orthogonal to a given set of arbitrary directions. They have been employed in the abstract interpretation of programs and, with particular success, in the reachability analysis of hybrid automata. While previously, the choice of directions has been left to the user or a heuristic, we present a method for the auto...

Received (received date) Revised (revised date) Communicated by Editor's name ABSTRACT In this paper we discuss eecient symbolic representations for innnite-state systems speciied using linear arithmetic constraints. We give algorithms for constructing nite automata which represent integer sets that satisfy linear constraints. These automata can represent either signed or unsigned integers and ...

The design of reliable embedded control systems inherits the difficulties involved in designing both control systems and distributed (concurrent) computing systems. Design bugs in these systems may arise from the unforeseen interactions among the computing, communication and control subsystems. Motivated by the difficulties of finding this type of design bugs, this thesis develops mathematical ...

Hybrid automata are often cited as the best model to describe and analyze controlcommand systems. However, no formal link exists between this high-level description and the low-level implementation of the control law (in C for example). In this article, we propose a framework that computes from a synchronous program an equivalent hybrid automata. To do this, we use an intermediate model, namely...

This report defines the syntax and formal semantics of the Chi 2.0 formalism. The Chi formalism integrates concepts from dynamics and control theory with concepts from computer science, in particular from process algebra and hybrid automata. It combines a high expressivity and ease of modeling with a formal semantics. The Chi language is defined by means of an abstract and a concrete syntax. Th...

In this paper we present a new symbolic approach to hybrid systems Hybrid systems are systems con taining both continuous and discrete changing quantities We model hybrid systems using hybrid automata Hybrid automata extend the classical notion of nite state machines by combining di erential equations to model the dynamic behavior of systems with a nite control In contrast to other approaches w...

Rectangular hybrid automata (RHA) are finite state machines with additional skewed clocks that are useful for modeling realtime systems. This paper is concerned with the uniform verification of safety properties of networks with arbitrarily many interacting RHAs. Each automaton is equipped with a finite collection of pointers to other automata that enables it to read their state. This paper pre...