Asymptotical stabilization of linear distributed parameter switched systems

In this paper, the asymptotical stabilization problem for ordinary differential equations switched systems has been extended to distributed parameter switched systems (DPSS) in Hilbert space. Based on semigroup and operator theory, sufficient conditions of asymptotical stabilization for linear DPSS are derived in linear operator inequalities (LOIs) framework. Being applied to three dimensional switched heat propagation equations, we transform the LOIs into the linear matrix inequalities (LMIs), which has the advantage of being numerically well tractable by using matlab software. In particular, the state feedback gain matrices are designed. Two examples are given to illustrate the proposed results.