A Floquet-like factorization for linear periodic systems

In this note, the novel representation is proposed for a linear periodic continuous-time system with T-periodic real-valued coefficients. We prove that a T-periodic real-valued factor and two real-valued matrix exponential functions can be extracted from a state transition matrix, while, in the wellknown Floquet representation theorem, a 2T-periodic realvalued factor and a real-valued matrix exponential function are extracted from the state transition matrix. Then we also proved that any T-periodic system can be transformed to a system with T-periodic real-valued trigonometric coefficients using a T-periodic real-valued coordinate transformation, while, in the well-known Lyapunov reducibility theorem, a 2T-periodic realvalued coordinate transformation is utilized to transform the given periodic system into a time-invariant system with real coefficients. This new information can be useful for designing a T-periodic control law. NOTATIONS R the set of all real numbers C the set of all co...

• Type: Conference
• Year: 2009
• Where: CDC
• Authors: Ichiro Jikuya, Ichijo Hodaka
• Keywords: CDC 2009, Control Systems, Matrix Exponential, Matrix Exponential Function, State Transition Matrix