Roesser Model Research Articles

Event-triggered sliding mode control for 2-D Roesser model with mismatched disturbance

This paper is concerned with designing two-dimensional event generators and sliding mode controllers for discrete-time two-dimensional systems described by the celebrated Roesser model with external mismatched disturbance. First of all, aimed at the characteristics of the Roesser model, the horizontal and vertical disturbance observers and sliding surface functions are established for the addressed two-dimensional systems, respectively. Then based on the disturbance estimation and rejection technique, a modified reaching law and its corresponding sliding mode controller are designed to achieve the system robustness and disturbance attenuation. To reduce the resource usage, the event-triggered strategy is further incorporated in the design of sliding mode control law. Moreover, the stability of the sliding-mode dynamics is analyzed by resorting to the Lyapunov stability theory. Finally, a simulation example is presented to verify the effectiveness of the proposed method.

Feasibility and stability of preview control for 2-D discrete-time systems described by the Roesser model

Feasibility and stability of preview control for 2-D discrete-time systems described by the Roesser model

Robust ∞ model reduction for the continuous fractional‐order two‐dimensional Roesser system: The 0 < ε ≤ 1 case

This study analyzes the model reduction methods and the robust model reduction methods for the continuous fractional‐order (FO) two‐dimensional (2D) Roesser system with the FO ranging from 0 to 1. A sufficient LMI‐based condition is given by Projection Lemma, the FO‐stable‐region‐analyze method and matrix analysis, guaranteeing that the error system is stable and that its transfer function's ‐norm is bounded. Then, the approach to design the reduced‐model system of the original continuous FO 2D Roesser model is given. The robust model reduction methods for continuous FO 2D Roesser systems with polytopic uncertainties are proposed based on the results above. In the end, two numerical examples are used to demonstrate the effectiveness of the results.

Stabilization of Switched Two Dimensional Fractional Order Positive Systems Modeled by the Roesser Model

Stabilization of Switched Two Dimensional Fractional Order Positive Systems Modeled by the Roesser Model

Transformation of Two-Dimensional Roesser Model Into Two-Dimensional Decoupled Model: Application to Model Reduction via Balanced Framework

Two transformations are presented in this research; the first approach takes a generic two-dimensional (2-D) framework and transforms it into a diagonalized 2-D framework without resorting to minimal rank-decomposition criteria. Afterward, it converts the diagonalized system into two subsystems (i.e., one-dimensional (1-D) cascaded systems). Moreover, the proposed transformation retains the symmetrical structure of the two decomposed subsystems. Likewise, the second transformation converts 1-D submodels to the balanced structure used for model reduction operations. The proposed model reduction approach efficiently performs the model reduction task on a given 2-D diagonalized model by utilizing optimal Hankel norm approximation. The numerical results demonstrate that the proposed transformations efficiently convert the standard 2-D framework to a diagonalized model form and develop a stable reduced-order model.

Finite Frequency H∞ Control of Fractional-Order Continuous–Discrete 2-D Roesser Models

The H∞ control problem of fractional-order continuous-discrete 2D Roesser models in the finite frequency is investigated in this paper. Firstly, based on the frequency-partitioning method and generalized Kalman–Yakubovič–Popov lemma, the finite frequency bounded real lemmas in form of linear matrix inequalities (LMIs) are proposed, which can be solved by LMI solvers immediately. Then, the H∞ state feedback controller is designed, and the existence conditions are established in form of bilinear matrix inequalities (BMIs). Moreover, by the provided iterative algorithm, these BMI-based conditions can be solved based on LMIs. Finally, the numerical examples are provided verify the validity of our results.

Guaranteed Cost Control for 2-D Uncertain Discrete State-Delayed Systems in Roesser Model Employing Actuator Saturation

Guaranteed Cost Control for 2-D Uncertain Discrete State-Delayed Systems in Roesser Model Employing Actuator Saturation

Overflow Oscillation Elimination in Fixed-Point 2D Digital Filters Based on the Roesser Model

This paper investigates the overflow oscillation elimination problem in the fixed-point two-dimensional (2D) digital filter (DF) based on Roesser model subjected to two’s complement overflow (TCO) nonlinearities. By utilizing the system information and behavior of TCO nonlinearities more effectively, a new global asymptotic stability (GAS) criterion for 2D DFs is presented. A comparison of the obtained criterion with existing criteria is made with the help of examples.

Iteration learning control for 2D linear discrete systems with randomly varying trail lengths

This paper considers the problem of randomly varying trial lengths of a class of two-dimensional (2D) linear systems represented by Roesser model, and two new iterative learning control (ILC) schemes are proposed. One is a conventional P-type control rule with a modified tracking error; the other is an ILC law with an iteration-average operator. Both learning control schemes are developed by a 2D stochastic variable to describe varying trial lengths. Under the Bernoulli distribution assumption and the initial state conditions, the convergence analysis is performed rigorously in the probability sense. Finally, illustrative examples have been provided to verify the theoretical results.

Asynchronous event-triggered guaranteed cost control of two-dimensional Markov jump Roesser systems

This paper deals with the problem of asynchronous event-triggered guaranteed cost control for two-dimensional Markov jump systems in Roesser model. The hidden Markov model is introduced to characterize the asynchronous phenomenon induced by imperfect mode detection, and a hidden Markov model-based event-triggered mechanism is employed in controller design to reduce the communication burden of the network. By using the quadratic Lyapunov function technique, some sufficient criteria are developed to ensure the asymptotic stability of the addressed system with a guaranteed cost value under three different boundary conditions. Finally, an optimization algorithm with linear matrix inequality constraints is formulated to design the optimal asynchronous event-triggered guaranteed cost control law, and a simulation example is considered to illustrate its validity.

Practical Exponential Stability of Two Dimensional Nonlinear Switched Positive Systems in the Roesser Model

Practical Exponential Stability of Two Dimensional Nonlinear Switched Positive Systems in the Roesser Model

H ∞ performance analysis for 2D discrete singular stochastic systems

This paper addresses the problem of H∞ performance analysis of 2D discrete singular stochastic system described by Roesser model which is challenging since it involves 2D random variables and the disturbance simultaneously. Sufficient conditions are established for the regularity, causality and stability of the system. The proposed results are expressed in terms of strict linear matrix inequalities. Furthermore, a mean square asymptotic stability with an H ∞ disturbance level is developed. Simulation example is provided in order to illustrate the relevance of our approach.

Zonotopic state bounding for 2-D systems with dynamic event-triggered mechanism

This paper investigates the problem of zonotope-based state estimation for 2-D systems represented by both the Fornasini–Marchesini local state–space (FMLSS) model and the Roesser model with dynamic event-triggered mechanism (ETM) where the exogenous disturbance and measurement noise are assumed to be unknown-but-bounded (UBB). First, considering the different characteristics of these two models, we design different dynamic ETMs for both FMLSS type and Roesser type respectively. A zonotopic set-membership estimation approach is proposed for the considered 2-D system to obtain the estimation interval. Then, three optimal observer design methods are proposed for different scenarios. In addition, the relationship of the proposed criteria is further discussed between the 2-D augmented error FMLSS system and the 2-D augmented error Roesser system considered in this paper. Finally, simulation results are given to illustrate the effectiveness of the proposed methods.

H∞ filtering for continuous fractional‐order 2D Roesser model: The 0<α≤1 case

AbstractThis paper investigates the filtering for the continuous fractional‐order (FO) two‐dimensional (2D) Roesser model with the FO between 0 and 1. Firstly, a sufficient condition to ensure the stability and bounded realness in the sense of ‐norm for the continuous FO 2D Roesser model is given in the form of linear matrix inequalities (LMIs). Secondly, based on the bounded real lemmas proposed above, the filtering problem for continuous FO 2D Roesser model is addressed through some congruent transformation and matrix transformation. The results are given in LMI form, and the parameters of the continuous FO 2D filters can be achieved from the LMIs easily. In the end, the effectiveness of the proposed results is verified by two numerical examples.

Admissible transformation approach to Roesser state‐space model realization of singular multidimensional systems

AbstractThe problem of the singular Roesser (state‐space) model realization of non‐causal multivariate transfer (function) matrices is investigated. Specifically, the notion of so‐called admissible transformation is introduced, which allows to introduce and investigate a novel invariant matrix relationship on polynomial matrices. The singular multidimensional Roesser model (SNDRM) realization is transformed to the problem of how to reduce an initial polynomial matrix associated with the given transfer matrix into the objective polynomial matrix with a specific structure. Construction procedures are developed to obtain SNDRMs by applying admissible transformations on the initial polynomial matrix. Moreover, a separated standard form is introduced for an SNDRM so that the proposed approach can effectively treat both the left and right matrix fractional descriptions of a non‐causal multivariate transfer matrix in a unified manner. Non‐trivial examples are provided to illustrate the details and effectiveness of the proposed approach.

New tests for the stability of 3D Roesser models

New tests for the stability of 3D Roesser models

Output tracking control for 2‐D discrete systems with actuator failures

AbstractThis article is concerned with the reliable output tracking control problem for a class of two‐dimensional (2‐D) discrete systems with actuator faults. The systems are described by the well‐known Roesser model. The aim of the problem addressed is to design a reliable controller such that the output of the 2‐D discrete systems tracks the output of a given reference model well in the sense. By resorting to a Lyapunov function and some zero equations, a new criterion on tracking performance analysis is presented. This criterion is then applied to design the tracking controller, for both cases known and unknown actuator failures. Finally, two examples are given to illustrate the effectiveness of the proposed method.

Hankel norm performance of 2-D digital filters described by Roesser model with overflow arithmetic

ABSTRACT This paper is concerned with the problem of asymptotic stability with Hankel norm performance (HNP) of two-dimensional (2-D) digital filter characterised by Roesser model, where the 2-D system includes overflow nonlinearities and external interference or excitation of finite duration. The underlying nonlinearities cover the usual types of overflow arithmetic utilised in practice such as saturation, two’s complement, zeroing and triangular. To solve this problem, new sufficient criterion is proposed by employing quadratic 2-D Lyapunov function. The proposed criterion guarantees that the addressed system has 2-D HNP bound. This criterion can examine the unwanted memory effect (ME) reduction of 2-D interfered digital filters for past excitations. In the absence of external inputs, the asymptotic convergence of 2-D digital filters is established under the proposed criterion. The developed HNP criterion is in linear matrix inequality framework and, therefore, computationally tractable. In addition, the optimisation problem is formulated to obtain the minimum HNP of the 2-D interfered digital filter. To illustrate the effectiveness of the proposed criterion, a numerical example is provided. The criteria addressed in current paper can give a whole analysis framework for the unwanted MEs of filters.

Disturbance Rejection Control for 2-D Roesser Model Under Event-Triggered Frameworks

Disturbance Rejection Control for 2-D Roesser Model Under Event-Triggered Frameworks

Zeroing the transfer matrix of the Roesser model of 2-D linear systems

Zeroing the transfer matrix of the Roesser model of 2-D linear systems