Constrained Control of Uncertain, Time-varying Linear Discrete-Time Systems Subject to Bounded Disturbances

Abstract

International audienceThe aim of this paper is twofold. In the first part, robust invariance for ellipsoidal sets with respect to uncertain and/or time-varying linear discrete-time systems with bounded additive disturbances is revisited. We provide an extension of an existing invariance condition. In the second part a novelrobust interpolation based control design involving several local unconstrained robust optimal controls is proposed. At each timeinstant a quadratic programming problem is solved on-line. Proofs of recursive feasibility and input-to-state stability are given

On the impact of additive disturbances on Auto-Steering Systems

“…For this construction, in spite of precomputing a stabilizing gain for the unperturbed system, the stabilizing gain computation is done at the same time as the RPI set computation, obtaining in this way a robust stabilizing gain that maximizes the RPI set, in which the input and output constraints are fulfilled in the presence of parameter-varying disturbances. This can be done by solving the following LMI problem (Nguyen et al, 2015) max P3,Yi,θ {θ + σtrace(P 3 )} (21) subject to:…”

Commutativity of first‐order discrete‐time linear time‐varying systems

“…Digital systems are modeled as discrete‐time systems. In the last decade, there is a great number of papers published in the famous journals, on the theory and applications of discrete‐time linear time‐varying systems . Therefore, it is very important to investigate the commutativity property for time‐varying discrete‐time systems as well.…”

“…In the last decade, there is a great number of papers published in the famous journals, on the theory and applications of discrete-time linear time-varying systems. [16][17][18][19][20][21][22][23][24][25][26][27][28][29] Therefore, it is very important to investigate the commutativity property for time-varying discrete-time systems as well. The paper emphasizes this importance and is aimed to be the first attempt to carry the theory developed for commutativity of analog systems 6 into discrete-time domain.…”

Robust output feedback control: Convex lifting based approach

“…As an extension, the Ngoc Anh Nguyen, Sorin Olaru are with the Laboratory of Signals and Systems (L2S, UMR CNRS 8506), CentraleSupélec-CNRS-UPS, Université Paris Saclay, 3 rue Joliot Curie, Plateau de Moulon, 91192, Gif-sur-Yvette, France. Ngocanh.Nguyen.rs@gmail.com, Sorin.Olaru@centralesupelec.fr interpolation based approach was put forward in [18], in which the interpolation gain serves as a control Lyapunov function. Accordingly, robust stability is ensured by the nonincrease of this gain along the dynamics.…”