Problems in the theory of $H^2/H_\infty$ controllers for linear stochastic multiplicative-type plants

This paper considers $H^2/H_\infty$ control problems for dynamic plants described by linear Itô stochastic equations with the drift and diffusion coefficients linearly dependent on the state vector, control input, and an exogenous disturbance. The controlled plant has two outputs, namely, the regulated $z$ and the observed (noisy) $y$ ones. The controller is optimized by the quadratic $H^2$ criterion under the boundedness condition for the induced norm of the operator $H_{zv}$ relating the exogenous disturbance $v$ to the regulated output $z: ||H_{zv}||_\infty<\gamma$. The conditional $H^2/H_\infty$ optimization problem is solved using differential game theory.