Well-posedness of bimodal state-based switched systems

On well-posedness of piecewise affine bimodal dynamical systems

The theory of differential inclusions provides certain sufficient conditons for the uniqueness of Filippov solutions such as one-sided Lipschitzian property or maximal monotone condition. When applied to piecewise affine dynamical systems, these conditions impose rather strong conditions. In this paper, we provide less restrictive conditions for uniqueness of Filippov solutions for the bimodal ...

Well-posedness of Hybrid Systems

Modelling, Well-Posedness, Stability of Switched Electrical Networks

A modeling framework is proposed for circuits that are subject to both time and state events. The framework applies to switched networks with linear and piecewise linear elements including diodes and switches. We show that the linear complementarity formulation, which already has proved effective for piecewise linear networks, can be extended in a natural way to cover also switching circuits. W...

Well{posedness of Stiff Hyperbolic Systems

The theory of stii well{posedness of initial value problems for hyperbolic systems with large relaxation terms is reviewed. Furthermore, an asymptotic expansion of solutions with respect to the relaxation parameter is presented. Finally, the theory is illustrated with an example and an outlook concerning boundary value problems is given.

Well-Posedness of Reset Control Systems as State-Dependent Impulsive Dynamical Systems

and Applied Analysis 3 see 4–6 . In general, there exists a unique solution ψ t eψ0 of the continuous base system with initial condition ψ 0 ψ0 on 0,∞ , for any ψ0 ∈ R. Informally speaking, the solution x of the IDS 2.1 from the initial condition x 0 x0 is given by x t ex0 for 0 < t ≤ t1, where t1 is the first resetting time satisfying x t1 ∈ M. Then, the state is instantaneously transferred to...