  This paper is concerned with the design of a linear control law for linear
systems with stationary additive disturbances. The objective is to find a state
feedback gain that minimizes a quadratic stage cost function, while observing
chance constraints on the input and/or the state. Unlike most of the previous
literature, the chance constraints (and the stage cost) are not considered on
each input/state of the transient response. Instead, they refer to the
input/state of the closed-loop system in its stationary mode of operation.
Hence the control is optimized for a long-run, rather than a finite-horizon
operation. The controller synthesis can be cast as a convex semi-definite
program (SDP). The chance constraints appear as linear matrix inequalities.
Both single chance constraints (SCCs) and joint chance constraints (JCCs) on
the input and/or the state can be included. If the disturbance is Gaussian,
additionally to WSS, this information can be used to improve the controller
design. The presented approach can also be extended to the case of output
feedback. The entire design procedure is flexible and easy to implement, as
demonstrated on a short illustrative example.
