Control synthesis of linear distributed parameter switched systems

The control synthesis for switched systems is extended to distributed parameter switched systems in Hilbert space. Based on semigroup and operator theory, by means of multiple Lyapunov method incorporated average dwell time approach, sufficient conditions are derived in terms of linear operator inequalities framework for distributed parameter switched systems. Being applied to one dimensional heat propagation switched systems, these linear operator inequalities are reduced to linear matrix inequalities subsequently. In particular, the state feedback gain matrices and the switching law are designed, and the state decay estimate is explicitly given whose decay coefficient completely depends on the system’s parameter and the boundary condition. Finally, two numerical examples are given to illustrate the proposed method.