Gain-Scheduled H∞ Control for Discrete-Time Polynomial LPV Systems Using Homogeneous Polynomial Path-Dependent Lyapunov Functions

Dynamic controllers for local input‐to‐state stabilization of discrete‐time linear parameter‐varying systems with delay and saturating actuators

“…Then, the closed-loop of the LPV system (1)- (2) with the linear parameter varying dynamical compensator (7) with…”

“…The main problem investigated in this article can be summarized as follows: Problem 1. Given the LPV system (1)-(6), determine the time-varying matrices of the linear parameter varying dynamical controller (7), and estimate   and   0 , such that for a given > 0 and all k ∈ , for all 0 ∈   0 , for all k ∈ Ξ, the closed-loop system (1)-(6) with (7) is (locally) ISS.…”

“…Consider the matrices A cij,h k ,  ij ,  ij C ci ,  i ,  i , and E ci of the compensator in (7). If there exist symmetric positive definite matrices W i, ∈ R n(h+1+ )×n(h+1+ ) , positive definite diagonal matrix S ∈ R m×m , matrices U ∈ R n(h+1+ )×n(h+1+ ) , Y i , H i ∈ R m×n(h+1+ ) , with i ∈  [1, N] and ∈ [h, h], and positive scalars and , satisfying…”

“…The objective is to design dynamic output feedback controllers that maximize the allowed energy disturbance, −1 , thus, ensuring that the trajectories of the closed-loop system remain in the estimated region of attraction. We have run the optimization procedure  2 given in (32) for maximum delay values h ∈  [1,7] and order of the dynamic output-feedback controller in the range n to (h + 1)n, that is, for ∈ [1, h + 1]. Additionally, we supposed a slow variation of the delay by taking Δh max = 1, thus meaning that among two consecutive instants, the delay must remain in its current value, increase by one, or reduce its value by one, but always keeping h k ∈ [0, 7].…”

“…1,2 As a consequence, the research on the control of LPV systems has been extensively explored and included in various engineering applications in the last decades. 3 Instead of using robust controllers, 4 stability and performance have been pursued through the development of parameter varying controllers, which can be linear 5,6 or rational [7][8][9][10] on the parameter. In all cases, the Lyapunov-based approach is used, which usually leads to convex optimization design methods.…”