MINIMAX CONTROL OF SWITCHING SYSTEMS UNDER SAMPLING

We consider a general class of systems subject to two types of uncerta inty: A continuous deterministic uncertainty that affects the system d ynamics, and a discrete stochastic uncertainty that leads to jumps in the system structure at random times, with the latter described by a c ontinuous-time finite state Markov chain. When only sampled values of the system state is available to the controller, along with perfect me asurements on the state of the Markov chain, we obtain a characterizat ion of minimax controllers, which involves the solutions of two finite sets of coupled PDEs, and a finite dimensional compensator. For the l inear-quadratic case, a complete characterization is given in terms of coupled generalized Riccati equations, which also provides the soluti on to a particular H-infinity optimal control problem with randomly sw itching system structure and sampled state measurements.