Ackermann-like eigenvalue assignment formulae for linear time-varying systems

Eigenvalue assignment techniques for linear time-varying systems are presented as a way of achieving feedback stabilisation. For this, novel eigenvalue concepts, which are the time-varying counterparts of conventional (time-invariant) eigenvalue ideas, are introduced. Ackermann-like formulae for both SISO and MIMO linear time-varying systems are proposed. It is believed that these techniques are the generalised versions of the Ackermann formulae for linear time-invariant systems. The advantages of the proposed Ackermann-like formulae are that they neither require the transformation of the original system into a phase-variable form nor the computation of the eigenvalues of the original system, and they can allow the closed-loop system to have desired eigenvalue trajectories rather than fixed eigenvalue locations. Two examples are given to demonstrate the capabilities of the proposed techniques.