Robust Control: The Parametric Approach

Robust Stabilization Of Interval Plants With Constant Disturbance

“…This results is similar to that in item ii) of Theorem 13.1 in [4]. However, the result in Proposition 3 does not require the stronger assumption that the coefficients of Γ m have the same sign.…”

“…Besides, α 11 = α 31 = α − and α 21 = α 41 = α + for σ 1 ; α 11 = α 41 = α − and α 21 = α 31 = α + for σ 2 ; α 11 = α 31 = α + and α 21 = α 41 = α − for σ 3 ; and α 11 = α 41 = α + and α 21 = α 31 = α − for σ 4 . By Lemma 5.3 in [4], for each polynomial 1 ( ) n j K s + there exists α j > 0 such that this polynomial is Hurwitz, for all σ j ∈ [0, α j ). Then, take α = min{α 1 , α 2 , α 3 , α 4 } and the result is proved.…”

“…Remark 3. Notice that, contrary to Theorem 13.1 in [4], the assumptions that the coefficients of Γ m have the same sign are not longer required. On the other hand, it is not required to stabilize several Kharitonov's plants as in Barmish et al [2], or to check the stability of 32 virtual polynomials as in Hernández and Dormido [9].…”

“…Since the Kharitonov's pioneering work [12], the robust stabilization problem of disturbance-free interval plants has received considerable attention [2,4,9,10]. Most results are devoted to proving the existence of a controller that stabilizes the whole family of plants.…”

“…The aim of this brief paper is to study the robust stabilization problem for the class of SISO interval plants defined by (1), (3). By extending some results from the area of parametric robust control [2,4,9], a characterization of output feedback controllers with integral action that stabilize a given interval plant family is obtained. A procedure to compute the corresponding control parameters is also discussed.…”