Pointwise minimum norm control laws for hybrid systems

Minimum-norm control laws for hybrid dynamical systems are proposed. Hybrid systems are given by differential equations capturing the continuous dynamics or flows, and by difference equations capturing the discrete dynamics or jumps. The proposed control laws are defined as the pointwise minimum norm selection from the set of inputs guaranteeing a decrease of a control Lyapunov function. The cases of individual and common inputs during flows and jumps, as well as when inputs enter through one of the system dynamics, are considered. Examples illustrate the results. ©2013 IEEE

On Notions of Output Finite-Time Stability

International audienceLyapunov characterizations of output finite-time stability are presented for the system $x' = f (x), y = h(x)$ which is locally Lipschitz continuous out of the set $Y = {x ∈ R n : h(x) = 0}$ and continuous on $R^n$. The definitions are given in the form of $K$ and $KL$ functions. Necessary and sufficient conditions for output finite-time stability are given using Lyapunov functions. The theoretical results are supported by numerical examples

On necessary and sufficient conditions for output finite-time stability

International audienceOutput global finite-time stability of locally Lipschitz continuous autonomous systems is characterized by means of smooth Lyapunov functions. The so-called output-Lagrange stable systems are studied with details. Influence of a kind of continuity of the settling-time function is considered. Necessary and sufficient conditions of output finite-time stability are presented. The theoretical results are supported by academic examples and numerical simulations

Finite Gain L p Stability for Hybrid Dynamical Systems ⋆

Abstract We characterize finite gain Lp stability properties for hybrid dynamical systems. By defining a suitable concept of hybrid Lp norm, we introduce hybrid storage functions and provide sufficient Lyapunov conditions for Lp stability of hybrid systems, which cover the well-known continuous-time and discrete-time Lp stability notions as special cases. We then focus on homogeneous hybrid systems and prove a result stating the equivalence among local asymptotic stability of the origin, global exponential stability, existence of a homogeneous Lyapunov function with suitable properties for the hybrid system with no inputs, and input-to-state stability, and we show how these properties all imply Lp stability. Finally we characterize systems with direct and reverse average dwell time properties and establish parallel results for this class of systems. We also make several connections to the existing results on dissipativity properties of hybrid dynamical systems