Robust sampled‐data controller design for uncertain nonlinear systems via Euler discretization

Abstract

Robust stabilization of a class of uncertain nonlinear systems through a sampled-data control law is considered in this work. Based on the forward discrete-time Euler approximation, conditions in the form of linear matrix inequalities are provided to synthesize a discrete controller that guarantees the states to be asymptotically driven to the origin, regardless of the presence of bounded parametric uncertainties. In contrast with other approaches, the system is not required to be Lure-type nor the conditions to have predefined gains to be tested. Examples are given to illustrate the effectiveness of the proposal.

A sufficient condition to design unknown input observers for nonlinear systems with arbitrary relative degree

“…It is clear that minimizing the trace of P enlarges the set ℰ , while the constraints P > 0 and ( 14) ensure that the ℰ is a positively invariant set, finally, the constraint (20) ensures the inclusion ℰ ⊂ 𝒟 ⊖ ℛ. The numerical results of this article are obtained by solving* the optimization problem (26) for obtaining the UIO gains L j = P −1 Lj , j ∈ B q and an enlarged set of admissible initial error ℰ . Notice that enlarging the set of admissible initial error ℰ is important to guarantee a reasonable estimation solution.…”

Event‐triggered control of quasi‐LPV systems with communication delays

“…Consider the closed-loop system (20) satisfying Assumptions 1 and 2, and let scalars h, 𝜖, 𝜌 ∈ R >0 , 𝜏 ∈ R ≥0 , and d = h + 𝜏 be given. If there exist symmetric matrices (34) and (35) and the following inequalities hold…”

“…Let scalars h, 𝜖, 𝜇, 𝜌, 𝜆 ∈ R >0 , 𝜂 0 , 𝜏 ∈ R ≥0 , 𝜃 ≥ (e 𝜆h − 1)∕𝜆, and d = h + 𝜏 be given. If there exist symmetric matrices P, Q, R, S, Ξ, Θ ∈ R n×n , and matrices (34) and (35) and the following inequalities hold…”

“…However, to ensure the correct control implementation, one needs to guarantee that the closed-loop trajectories remain confined inside the region where the polytopic model is valid. 35,36 This issue can be solved by determining a guaranteed region of attraction estimation contained in the region of validity. Unfortunately, this aspect is neglected by the majority of papers on ETC of quasi-LPV or TS fuzzy models, a few exceptions are for instance.…”

Gain‐scheduled control design for discrete‐time nonlinear systems using difference‐algebraic representations

“…In some real‐world control applications, constraints on the control inputs and states may be required to be fulfilled for physical, technical, or safety reasons 6 . Input constraints usually arise from actuators saturation 7‐10 . On the other hand, besides the necessity to obey physical and safety requirements, system states are, sometimes implicitly, assumed to be bounded in order to guarantee the validity of underlying mathematical models used to solve analysis and/or synthesis control problems 11 .…”