A less conservative robust stability criteria for uncertain neutral systems with mixed delays

New mixed‐delay‐dependent robust stability conditions for uncertain linear neutral systems

“…Therefore, over the past more than 10 years, various techniques have been developed to produce some delay-dependent stability and control design conditions, such as the bounding inequality for the cross term [5], descriptor model transformation [6][7][8][9], integral inequality methods [10,11], free-weighting matrix techniques [10,[14][15][16][17], augmented L-K functionals [17,[19][20][21][22], delay-decomposition approaches [12,23,24] and complete L-K functional approach [13,25]. Compared with the results in [13,25], the conditions in [5][6][7][8][9][10][11][12][14][15][16][17][18][19][20][21][22][23][24] are based on the simple L-K functionals, and remain conservative to some extent. However, the conditions in [5][6][7]…”

A GGP approach to solve non convex min-max predictive controller for a class of constrained MIMO systems described by state-space models

“…Positively signed term (c > 0): If we consider the ∑ ∏ (17) The latter signomial in the right hand is now convex relatively to zi according to Property 1. This transformation is referred to as the exponential transformation.…”

“…In fact, a new criterion is obtained where all negative signed terms are convex and new constraints are added. In the on-line algorithm, only exponential transformations are applied to the positively signed terms (see (17)). In this case, new non linear constraints in the number of the monomial variables appear.…”

“…The class of predictive control methods that explicitly account for the modeling errors (or uncertainties) is Robust Model Predictive Control (RMPC). This type of MPC has been thoroughly investigated for many years (see e.g [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]). One widely used technique for improving robustness in MPC consists of the min-max optimization [20] where a quadratic cost function is minimized with respect to its worst-case, the latter being taken over the set of all possible plant uncertainties.…”

Improved conditions for neutral delay systems with novel inequalities

“…Various interesting methods have been introduced to obtain delay-dependent stability conditions for neutral delay systems, such as model transformation approach [8], delay partitioning technique [2], discretized Lyapunov functional method [11], free-weighting matrix approach [9,12], and integral inequality method [1]. With the help of these approaches, improved delay-dependent stability conditions have been presented gradually, such as [3,11,15] and the references therein. It is known that Jensen's like inequalities have played an important role in obtaining delay-dependent stability conditions.…”