# DISCONTINUOUS RIGHT-HAND SIDES : FILIPPOV SOLUTIONS , NONSMOOTH STABILITY AND DISSIPATIVITY THEORY , AND OPTIMAL DISCONTINUOUS FEEDBACK CONTROL

@inproceedings{Haddad2014DISCONTINUOUSRS, title={DISCONTINUOUS RIGHT-HAND SIDES : FILIPPOV SOLUTIONS , NONSMOOTH STABILITY AND DISSIPATIVITY THEORY , AND OPTIMAL DISCONTINUOUS FEEDBACK CONTROL}, author={Wassim M. Haddad}, year={2014} }

In this paper, we develop stability, dissipativity, and optimality notions for dynamical systems with discontinuous vector fields. Specifically, we consider dynamical systems with Lebesgue measurable and locally essentially bounded vector fields characterized by differential inclusions involving Filippov set-valued maps specifying a set of directions for the system velocity and admitting Filippov solutions with absolutely continuous curves. In addition, we extend classical dissipativity theory…

## 6 Citations

Universal Feedback Controllers and Inverse Optimality for Nonlinear Stochastic Systems

- Computer ScienceJournal of Dynamic Systems, Measurement, and Control
- 2019

A constructive finite time stabilizing feedback control law for stochastic dynamical systems driven by Wiener processes based on the existence of a Stochastic control Lyapunov function is developed.

Universal Feedback Controllers and Inverse Optimality for Nonlinear Stochastic Systems

- Computer Science2019 IEEE 58th Conference on Decision and Control (CDC)
- 2019

A constructive finite time stabilizing feedback control law for stochastic dynamical systems driven by Wiener processes based on the existence of a Stochastic control Lyapunov function is developed.

Condensed matter physics, hybrid energy and entropy principles, and the hybrid first and second laws of thermodynamics

- Physics, Computer ScienceCommun. Nonlinear Sci. Numer. Simul.
- 2020

An energy-based, large-scale hybrid dynamical system model is developed to present a generic framework for hybrid thermodynamics involving hybrid energy and entropy conservation and nonconservation principles and to provide hybrid extensions to the first and second laws of thermodynamics.

Complexity, Robustness, and Multistability in Network Systems with Switching Topologies: A Hierarchical Hybrid Control Approach

- Computer Science
- 2015

Control algorithms were developed to address agent interactions, cooperative and non-cooperative control, task assignments, and resource allocations and appropriate sensory and cogitative capabilities such as adaptation, learning, decision-making, and agreement on the agent and multiagent levels were developed.

Human Brain Networks: Spiking Neuron Models, Multistability, Synchronization, Thermodynamics, Maximum Entropy Production, and Anesthetic Cascade Mechanisms

- Mathematics, Computer ScienceEntropy
- 2014

Lyapunov-based tests for multistability and synchronization of dynamical systems with continuously differentiable and absolutely continuous flows are established and the results are applied to excitatory and inhibitory biological neuronal networks to explain the underlying mechanism of action for anesthesia and consciousness from a multistable dynamical system perspective.

Thermodynamics: The Unique Universal Science

- Computer Science, PhysicsEntropy
- 2017

The history of thermodynamics is traced from its classical to its postmodern forms, and a tutorial and didactic exposition of thermodynamic principles as it pertains to some of the deepest secrets of the universe are presented.

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