Arbitrary eigenvalue assignment via switching hyperplanes design scheme and extension of Ackermann's formula

The system considered is assumed to be linear time invariant and completely state controllable. First, a formula is presented for the design of switching hyperplanes in the sliding-mode control (SMC) of multivariable systems. According to the desired closed-loop eigenvalues, sliding hyperplanes are directly determined. Next, a systematic scheme to arbitrarily assign closed-loop eigenvalues of multivariable systems is achieved. For the case of single variable, the proposed scheme reduces to the well-known Ackermann's formula.<<ETX>>