On the flexibility offered by state feedback in multivariable systems beyond closed loop eigenvalue assignment

An Optimal Augmented Monotonic Tracking Controller for Aircraft Engines with Output Constraints

“…Hence, the invariant zeros of system s  and sa  are the same.□ For definiteness and without loss of generality, Assumption 3 is replaced by the following Assumption 4: (9) where I t 1 and I t 2 are the matrices formed by I m , I n and I p s , which can be expressed as:…”

“…In recent years, a method was designed to avoid overshoot for linear time invariant (LTI) systems [8]. This method, employing the classic eigenstructure assignment algorithm of [9], can achieve arbitrarily fast settling times while guaranteeing a non-overshooting response in all components of the output vector for any initial condition. A modified approach is developed to prevent the step response from undershoot [10].…”

Non-iterative pole placement technique: A step further

“…It means that the sets L, X and Z are closed under conjugation and therefore so are the sets of eigenvectors. See [15] for details about how to obtain a real K and to reduce numerical effects of imaginary parts.…”

“…Condition (iii) corresponds to the actual assignment equality and encompasses v j 2 S j , u i 2S i and Eq. (15). The problem therefore appears to be essentially bilinear since X and Z have to be found so that to check Eq.…”

“…Eigenstructure is a concept that reveals particularly useful to design pole placement through direct computation. The next reasoning, borrowed from [15], is a basis for this contribution. The spectrum of A c is associated to right eigenvectors v i by the relations…”