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In this paper we present a new method for approximating the matrix exponential of a Metzler matrix. This method is useful in discretising switched positive systems. In particular, the method preserves both linear and quadratic stability of the original continuous time system, as well as positivity of states starting for initial conditions in the positive orthant. The usefulness of the method is highlighted...
This paper deals with the problem of finding a lower bound for the optimal value of a quadratic cost functional for a continuous-time autonomous linear switched system. This bound is computed on the basis of a set of matrices that satisfies some mild assumptions. An admissible set can be derived directly from the piecewise quadratic Lyapunov function used to construct a stabilizing conic switching...
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