  This paper is concerned with a stochastic linear-quadratic (LQ) optimal
control problem on infinite time horizon, with regime switching, random
coefficients, and cone control constraint. Two new extended stochastic Riccati
equations (ESREs) on infinite time horizon are introduced. The existence of the
nonnegative solutions, in both standard and singular cases, is proved through a
sequence of ESREs on finite time horizon. Based on this result and some
approximation techniques, we obtain the optimal state feedback control and
optimal value for the stochastic LQ problem explicitly, which also implies the
uniqueness of solutions for the ESREs. Finally, we apply these results to solve
a lifetime portfolio selection problem of tracking a given wealth level with
regime switching and portfolio constraint.
