In this paper the class of linear impulsive systems is considered. These systems are those with a continuous linear dynamics for all time, except at a sequence of instants. When such a discrete time occurs, the state undergoes a jump, or more precisely follows a discrete linear dynamics. The sequence of time instants, when a discrete dynamics occurs, is nearlyperiodic only, i.e. it is distant f...

The hybrid control systems considered here consist of a continuous-time plant under the control of a discrete event system. Communication between the plant and controller is provided by an interface which can convert signals from the continuous domain of the plant to the discrete, symbolic domain of the controller, and vise-versa. When designing a controller for a hybrid system, the designer ma...

Several recent results in the area of robust asymptotic stability of hybrid systems show that the concept of a generalized solution to a hybrid system is suitable for the analysis and design of hybrid control systems. In this paper, we show that such generalized solutions are exactly the solutions that arise when measurement noise is present in the system.

In this contribution, we consider a class of hybrid systems with continuous dynamics and jumps in the continuous state (impulsive hybrid systems). By using a newly elaborated version of the Pontryagintype Maximum Principle (MP) for optimal control processes governed by hybrid dynamics with autonomous location transitions, we extend the necessary optimality conditions to a class of Impulsive Hyb...

In this paper we consider the problem of extracting an abstraction from a hybrid control system while preserving timed languages. Such consistent abstractions are clearly useful as the abstracted, higher level model could be used for controller synthesis or verification of the more complicated lower level model. The class of abstracting maps we consider in this paper compress only the continuou...

Slope-parametric hybrid automata (SPHA) are hybrid automata whose variables can have parametric slopes. SPHA are useful, in particular, for modeling task-control systems in which the task speeds can be adjusted for meeting some safety requirement. In this paper, we present an example of parametric analysis for a simple task system. We introduce a prototype veriication tool that fully automates ...

In this work we develop an approach for the synthesis of the timed control of a class of hybrid systems modeled by rectangular hybrid automata. Our approach is within an automatic control view and is based on the reachable state spaces computation for any location. It consists of two steps, the first one being the computation of the control and the second being a step of the control propagation.

Abstraction is a natural way to hierarchically decompse the analysis and design of hybrid systems. Given a hybrid control system and some desired properties, one extracts and abstracted system while preserving the properties of interest. Abstractions of purely discrete systems is a mature area, whereas abstractions of continuous systems is a recent activity. In this paper we present a framework...