In this paper, by use of the properties of matrix measure, a set of linear and quadratic conditions is obtained which is sufficient for stabilizability of switched linear systems. These conditions are easily applicable because of their special form. So they are suitable to apply specially for higher order systems with several subsystems. Moreover, different system performances can also be achieved by using an appropriate objective function subject to the proposed conditions. In this way, an optimization problem is also introduced to stabilize the system with sub-optimal convergence rate. Finally a numerical example is used to show the effectiveness of the proposed approach.

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