We mainly focus on the derivation of less conservative sufficient conditions for the system to achieve certain performance.
As a first step, sufficient and generally conservative conditions expressed in terms of linear matrix inequalities (LMI) are provided.
By constructing a newly augmented Lyapunov-Krasovskii functional, less conservative sufficient stability conditions of the concerned systems are introduced within the framework of linear matrix inequalities (LMIs).
Therefore, a less conservative sufficient conditions in terms of linear matrix inequality (LMI) can be derived to design a more robust MPC algorithm.
The result provides a set of progressively less conservative sufficient conditions for proving positivity of fuzzy summations; such conditions are less and less conservative as a complexity parameter, n, increases.
In addition, a memory state feedback controller with input constraints yields less conservative sufficient conditions in terms of LMIs and allows for a wider feasible region of numerical optimization [13].
Based on these new summation inequalities, the reciprocally convex combination inequality, and a new Lyapunov-Krasovskii functional, a less conservative sufficient criterion on asymptotical stability of discrete-time systems with variable delays is obtained.
By incorporating the novel l2−l∞ performance analysis approach, the augmented piecewise Lyapunov-like functionals, the discrete Wirtinger-based inequality and the average-dwell-time switching, less conservative sufficient conditions are proposed by means of linear matrix inequalities.
First, by constructing Lyapunov-Krasovskii functional, a less conservative sufficient condition is obtained which guarantees that the closed-loop system is regular, impulse free, stable and robust strictly passive.
Based on such an approach, the less conservative sufficient conditions are established in terms of linear matrix inequalities under which the L2 L∞ performance level can be achieved for the estimation error dynamics.
