Well-posedness and Conservativity for Linear Control Systems (Part 2)

Well-posedness for General 2

We consider the Cauchy problem for a strictly hyperbolic 2 2 system of conservation laws in one space dimension u t + F (u)] x = 0; u(0; x) = u(x); (1) which is neither linearly degenerate nor genuinely non-linear. We make the following assumption on the characteristic elds. If r i (u); i = 1; 2; denotes the i-th right eigenvector of DF (u) and i (u) the corresponding eigenvalue, then the set f...

Linear complementarity systems: modelling power and well-posedness

Technological innovation pushes towards the consideration of dynamical systems of a mixed continuous and discrete nature, which are called “hybrid systems.” Hybrid systems arise, for instance, from the combination of an analog continuous-time process and a digital timeasynchronous controller. Many consumer products (cars, micro-wave units, washing machines and so on) are controlled by digital e...

On solution concepts and well-posedness of linear relay systems

In this paper we study the well-posedness (existence and uniqueness of solutions) of linear relay systems with respect to two di5erent solution concepts, Filippov solutions and forward solutions. We derive necessary and su7cient conditions for well-posedness in the sense of Filippov of linear systems of relative degree one and two in closed loop with relay feedback. To be precise, uniqueness of...

Characterization of well-posedness of piecewise-linear systems

One of the basic issues in the study of hybrid systems is the well-posedness (existence and uniqueness of solutions) problem of discontinuous dynamical systems. The paper addresses this problem for a class of piecewise-linear discontinuous systems under the definition of solutions of Carathéodory. The concepts of jump solutions or of sliding modes are not considered here. In this sense, the pro...

Well-posedness of Hybrid Systems