EXPONENTIAL DISSIPATIVITY OF DIFFUSION PROCESSES WITH MARKOVIAN SWITCHING AND ROBUST SIMULTANEOUS
The paper considers a class of systems composed of a finite set of controlled Ito diffusion processes with jumping transition between them determined by a homogeneous Markov chain. A new notion of stochastic exponential dissipativity is defined and some properties of exponentially dissipative diffusion processes with Markovian switching are studied. Connection between stochastic exponential dissipativity and
stabilization via output feedback is investigated. The obtained results are applied to robust simultaneous stabilization of a set of nonlinear uncertain systems.
It is shown that exponential dissipativity approach allows to obtain stability margin of robust system. The linear robust simultaneous stabilization problem is also considered as a particular case, in which a convergent algorithm for obtaining of output feedback gain is proposed and LMI based procedure for checking of stability margin is given. A numerical example is considered