1997 Volume 33 Issue 1 Pages 28-34
This paper is concerned with the problem of quadratic stabilization by decentralized control for a class of interconnected discrete-time systems with time-varying uncertainties both in the subsystem parameters and in the interconnections. We first show that the problem of quadratic stability for the interconnected systems can be reduced to the problem of the quadratic stability with disturbance attenuation for each subsystem. And utilizing this fact we derive a decentralized quadratic stabilizability condition and a decentralized state feedback gain in the case that the uncertainties in the subsystem parameters are norm-bounded. Since the stabilizability condition for each subsystem is independent each other, the control law may be effortlessly and efficiently designed. The condition is also transformed into linear matrix inequalities (LMI) for practical use.
