Robust constrained control by quadratic stability

The authors give preliminary results on the problem of robust control under various kinds of structural uncertainty and some constrained control cases, namely the static and dynamic output control and decentralized control. They first establish a necessary and sufficient condition for quadratic stabilizability of uncertain linear systems by means of full linear state feedback. An associated parametrical convex optimization problem is then presented. Its solution not only tests the stability condition but also provides a stabilizing gain. Another result, related to the H^∞ norm constraint, is given; it also makes use of the same type of convex optimization problem and is a practical method for H^∞ control synthesis for uncertain systems. Static or dynamic control with a H^∞ norm bound constraint is a new result. The decentralized control problem is also briefly discussed, and it is shown that all the results can also be extended to this case