Identifying the set of all admissible disturbances: discrete-time systems with perturbed gain matrix

Self Cite

The regulator problem for both discrete-time and continuous-time linear systems is considered. The control and its increments are under non-symmetrical constraints and the domain of constraints includes the origin on its boundary. We derive necessary and sufficient conditions which ensure the satisfaction of all the constraints and also the asymptotic stability by a state feedback. An illustrative example shows the application of our method.

Section: Introductionmentioning

confidence: 99%

Further results on the regulation problem for linear systems with constraints on control and its increment

Abdelhak,

Ou-azzou

2023

Self Cite

“…The maximal output sets (MOS) are of interest for the analysis of controlled constrained systems. Recently, maximal output set has been characterized for observability and asymptotically stable systems in the case of linear discrete-time systems (see [17][18][19][20][21]), this concept allows the comprehension of the analysis of constrained control systems. In addition, it is applied in control system design techniques [22].…”

Section: Introductionmentioning

confidence: 99%

On the maximal output set of fractional-order discrete-time linear systems

Bhih¹,

Benfatah²,

Ghazaoui³

et al. 2022

In this paper, we consider a linear discrete-time fractional-order system defined by \[\Delta ^{\alpha }x_ {k+1}=Ax_k+B u_k, \quad k \geq 0, \quad x_{0} \in \mathbb{R}^{n};\] \[y_{k}=Cx_k, \quad k \geq 0,\] where $A$, $B$ and $C$ are appropriate matrices, $x_{0}$ is the initial state, $\alpha$ is the order of the derivative, $y_k$ is the signal output and $u_k=K x_k$ is feedback control. By defining the fractional derivative in the Grunwald–Letnikov sense, we investigate the characterization of the maximal output set, $\Gamma(\Omega)=\lbrace x_{0} \in \mathbb{R}^{n}/y_{i} \in \Omega,\forall i \geq 0 \rbrace$, where $\Omega\subset\mathbb{R}^{p}$ is a constraint set; and, by using some hypotheses of stability and observability, we prove that $\Gamma(\Omega)$ can be derived from a finite number of inequations. A powerful algorithm approach is included to identify the maximal output set; also, some appropriate algorithms and numerical simulations are given to illustrate the theoretical results.

On the asymptotic output sensitivity problem for a discrete linear systems with an uncertain initial state

Rhila¹,

Lhous²,

Rachik³

2020

This paper studies a finite-dimensional discrete linear system whose initial state $x_0$ is unknown. We assume that the system is augmented by two output equations, the first one $z_i$ being representing measurements made on the unknown state of the system and the other $y_i$ being representing the corresponding output. The purpose of our work is to introduce two control laws, both in closed-loop of measurements $z_i$ and whose goal is to reduce asymptotically the effects of the unknown part of the initial state $x_0$. The approach that we present consists of both theoretical and algorithmic characterization of the set of such controls. To illustrate our theoretical results, we give a number of examples and numerical simulations.