  Here we use polynomial chaos framework to design controllers for linear
parameter varying (LPV) dynamical systems. We assume the scheduling variable to
be random and use polynomial chaos approach to synthesize the controller for
the resulting linear stochastic dynamical system. The stability of the LPV
system is formulated as an exponential mean-square (EMS) stability problem. Two
algorithms are presented that guarantee EMS stability of the stochastic system
and correspond to parameter dependent and independent Lyapunov functions,
respectively. LPV controllers from the polynomial chaos based framework is
shown to outperform LPV controller from classical design for an example
nonlinear system.
