Titlebook: Switching in Systems and Control; Daniel Liberzon Textbook 2003 Birkhäuser Boston 2003 Algebra.Lie-Algebra.Nonlinear system.algorithm.algo

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Stability under Arbitrary SwitchingGiven a family of systems (1.1), we want to study the following question: when is the switched system (1.3) asymptotically stable for every switching signal σ? We are assuming here that the individual subsystems have the origin as a common equilibrium point.

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LAIR

Systems with Sensor or Actuator ConstraintsIt is well known that switching control laws arise in time-optimal control of systems with controls taking values in bounded sets. For such systems, time-optimal control laws switch between boundary points of the admissible control set (hence the name “bang-bang controls”).

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Systems Not Stabilizable by Continuous Feedbackght happen that, while every state can be steered to the origin by some control law, these control laws cannot be patched together in a continuous fashion to yield a globally defined stabilizing feedback. In this section we discuss how this situation can occur.