Roesser Model Research Articles

Static output feedback control for positive 2D discrete systems in Roesser model

Abstract This paper investigates the output stabilization problem for multi-input multi-output positive 2D systems described by a linear discrete-time Roesser system. This kind of systems have the property that the horizontal and vertical states take non-negative values whenever the initial boundaries are non-negative. Conditions for the existence of desired static output feedback controllers guaranteeing the resultant closed-loop system to be positive and asymptotically stable are obtained. Also, the synthesis of static output feedback controllers, including the requirement of positivity of the controllers, is solved. These results are then extended to the case of uncertain plants. All of the proposed conditions are expressed in terms of Linear Programming, which can be easily verified by using standard numerical software. Finally, several numerical examples are included to illustrate the validity and the effectiveness of the developed results.

[formula omitted] security control for 2-D switched time delay systems under arbitrary delay time-variation rate and stochastic cyber attacks

This study focuses on H∞ security control for 2-D switched time delay systems subject to stochastic cyber attacks by the Roesser model, where the delay time-variation rate can be arbitrary. First, the time-delay system is modeled as the feedback interconnection of the delay-less system. To guarantee the security of the system under stochastic cyber attacks, a state-dependent switching signal and an anti-deception attack controller are constructed. Stability conditions of 2-D delay-less feedback interconnection systems are given for the first time. Then, for the considered system, some criteria based on bilinear matrix inequalities (BMIs) are established via the Lyapunov function technology such that the mean-square asymptotic stability with H∞ performance is guaranteed under arbitrary delay time-variation rate. Moreover, a cone-complement linearization (CCL) method is proposed to compute the optimized controller gains for BMIs. The effectiveness of the proposed method is validated via two numerical simulations.

Asynchronous sliding‐mode control for two‐dimensional nonlinear Markov jump systems with time‐varying delays

AbstractBased on the Roesser model, the asynchronous sliding‐mode control (SMC) problem for two‐dimensional (2‐D) Markov jump systems (MJSs) with time‐varying delays is studied in this article. Since the controller mode cannot always access the system mode, the asynchronous phenomenon between the system mode and the controller mode will be described by the hidden Markov model (HMM). First, under the framework of HMM, the asynchronous 2D‐SMC law is designed based on 2‐D sliding surface function to ensure closed‐loop 2‐D discrete MJSs asymptotic mean square stability and the reachability of sliding regions around specific sliding surfaces. Second, an algorithm for deducing the law of 2‐D asynchronous SMC is presented. Finally, a numerical example is given to verify the effective of the results.

On the positivity and asymptotic stability of the fractional 2D hybrid linear Roesser model

The aim of this paper is to introduce a new 2D fractional hybrid linear system described by the Roesser model with the conformable fractional derivative in the continuous time variables and the fractional difference in the discrete part. The solution of the considered model is derived. The positivity conditions are then extracted and the Cayley–Hamilton theorem is extended. A new necessary and sufficient conditions for the asymptotic stability of the proposed positive fractional 2D hybrid linear model are then established. Finally, some numerical examples are presented to show the applicability and the effectiveness of the presented methods.

Linear quadratic optimal control of stochastic 2-D Roesser models

This paper investigates the linear quadratic (LQ) optimal control problem for the stochastic two-dimensional (2-D) systems governed by Roesser models with multiplicative noise. The main contribution is to give the necessary and sufficient optimality condition by proposing a set of novel forward and backward stochastic partial difference equations (FBSPDE), and to further present the explicitly optimal feedback control laws on the finite horizon and on the infinite horizon based on the Riccati-like difference equations and the algebraic equation, respectively. Several numerical simulations are provided to illustrate the performance of the designed controllers.

Stabilization for 2-D switched T–S fuzzy systems under the state-dependent switching

This study focuses on the analysis of stability and stabilization for a class of two-dimensional (2-D) discrete-time switched systems. Owing to the inherent uncertainty and nonlinearity in real-world engineering systems, the Takagi–Sugeno (T–S) fuzzy model is employed to describe the dynamics of the 2-D switched system. The discussion encompasses two primary models for the 2-D discrete-time switched T–S fuzzy system (2DSTSFS), specifically the Roesser model and the Fornasini–Marchesini local state-space model. For 2DSTSFSs, this paper delineates sufficient stability criteria that utilize a state-dependent switching signal, facilitated by the application of the Lyapunov–Metzler inequality, ensuring that state trajectories are globally attracted. Furthermore, the paper articulates sufficient conditions for the stabilization of the 2DSTSFS. Additionally, it elucidates the transformation relationship between the two models. To corroborate the theoretical findings, a practical example is employed, demonstrating the applicability of the proposed theorems.

Asynchronous Control of 2-D Markov Jump Roesser Systems With Nonideal Transition Probabilities.

This article intends to study the asynchronous control problem for 2-D Markov jump systems (MJSs) with nonideal transition probabilities (TPs) under the Roesser model. Two practical considerations motivate the current work. First, considering that the system mode cannot always be observed accurately, a hidden Markov model (HMM) is adopted to describe the relationship between the mismatched modes. Second, considering that the TPs information related to the Markov process and the observation process is difficult to obtain, the nonideal TPs (unknown or uncertain) are simultaneously considered on the two processes. Under the considerations, several new sufficient conditions are developed for concerned closed-loop 2-D MJSs with nonideal TPs, by which the asymptotic mean square stability is ensured with an H∞ performance index. A nonconservative separation strategy is utilized to decouple the system mode TPs and the observation TPs to facilitate the analysis of nonideal TPs. An unified LMI-based condition is finally developed for the concerned closed-loop 2-D MJSs with/without nonideal TPs, showing more satisfactory conservatism than that in the literature. In the end, we present two examples to validate the superiority of the proposed design method.

Robust iterative learning control for discrete-time systems with random initial state shifts

This paper presents the sufficient conditions of the stability for discrete-time systems with random initial state shifts when applying iterative learning control. Different sufficient conditions have been developed for systems with different characteristics to ensure boundedness of tracking errors and convergence of the learning process under random initial condition. First, the relationship between the initial shifts of two adjacent iterations is addressed with the help of the transition matrix. And the different analysis models are established for each type of systems: one-dimensional matrix analysis model and 2-D Roesser model. Second, the new and sufficient conditions are established for the proposed learning control law to ensure systems convergence by matrix theory and two-dimensional system theory. Third, solving the linear matrix inequality (LMI) yields the control gains. Finally, digital simulations illustrate the effectiveness and sufficiency of the presented conditions.

Dynamic event‐triggered control of 2‐D continuous systems in Roesser model

AbstractIn this paper, a dynamic event‐triggered control problem is discussed for 2‐D continuous systems by the Roesser model. In order to reduce communication frequency and avoid dependence on global information, a dynamic event‐triggered mechanism is constructed, which is more flexible than some existing event‐triggered schemes with fixed event‐triggered thresholds. Utilizing the dynamic event‐triggered mechanism, a state feedback controller is designed. By constructing a 2‐D Lyapunov function, sufficient conditions expressed in terms of linear matrix inequalities (LMIs) are firstly established such that the 2‐D system is asymptotically stable with a disturbance attenuation performance. It is also proved that the Zeno phenomenon is excluded. Finally, two examples are provided to illustrate the effectiveness of the proposed method.

First- and Second-Order Sliding Mode Control Design for Networked 2-D Systems Under Round-Robin Protocol.

This article investigates the sliding mode control (SMC) problem for a class of uncertain 2-D systems described by the Roesser models with a bounded disturbance. In order to reduce the communication usage between the controller and the actuators, it is supposed that only one actuator node can gain the access to the network at each sampling time along horizontal or vertical direction, where a proper 2-D round-robin protocol is designed to periodically regulate the access token and a set of zero-order holders (ZOHs) is employed to keep the other actuator nodes unchanged until the next renewed signal arrives. Based on a novel 2-D common sliding function, a token-dependent 2-D SMC scheme with first-order sliding mode is appropriately constructed to cope with the impacts from the periodic scheduling signal and the ZOHs. Furthermore, a novel super-twisting-like 2-D SMC scheme with second-order sliding mode is designed to improve the robustness against the bounded disturbance. By resorting to token-dependent Lyapunov-like function, sufficient conditions are obtained to guarantee the ultimate boundedness of the horizontal and vertical states as well as the 2-D common sliding function. For acquiring the optimized gain matrices, two searching algorithms are formulated to solve two optimization problems arising from finding optimized control performance. Finally, two comparative examples are exploited to demonstrate the effectiveness and the advantageous of the proposed first- and second-order 2-D SMC design schemes under round-robin scheduling mechanism.

Stabilization of discrete‐time 2‐D switched systems: A state‐segmentation‐based event‐triggered mechanism

AbstractThis article addresses the event‐triggered control issue for two‐dimensional (2‐D) discrete‐time switched systems represented by both the Fornasini‐Marchesini local state‐space model and the Roesser model. The presence of 2‐D properties poses several challenges in selecting states for transport. Unlike existing event‐triggered generators, this article leverages the unique characteristics of 2‐D switched systems by dividing the system state into “horizontal” and “vertical” states. The segmented state is then transmitted at “necessary” two‐dimensional moments to minimize the amount of transmitted data. Furthermore, a state feedback controller, consisting of transferred horizontal and vertical states, is designed corresponding to the event‐triggered generator. By introducing average dwell time with the switching Lyapunov functional method, sufficient stabilization conditions are derived for the considered system. Finally, the proposed approach's effectiveness and improvement are illustrated by an example.

H∞ Control for 2D Singular Continuous Systems

This paper considers the problem of admissibility and admissibilization of 2D singular continuous systems described by the Roesser model. A necessary and sufficient admissibility condition is first proposed for 2D singular continuous systems in terms of a strict Linear Matrix Inequality (LMI). Then, a necessary and sufficient condition is established for the closed-loop system to be admissible (i.e., stable, regular, and impulse-free). Moreover, the stability condition is completed to give a sufficient condition to ensure a specified H∞ disturbance attenuation level for the state feedback closed loop. To illustrate the effectiveness of the proposed methodology, a numerical example is given to illustrate an admissibilization of a state feedback closed-loop system.

Finite region stability and networked predictive control for 2-D nonlinear time-delayed systems with quantization, packet dropouts and random disturbances

In this paper, we focus on the finite region stability (FRS) and networked predictive control (NPC) problems for two-dimensional (2-D) networked control systems (NCS) with time delays, quantization errors, packet losses and random disturbances described by the Roesser model. The random packet dropouts and disturbances are modeled as Bernoulli process, and the sufficient conditions of FRS and finite region boundedness (FRB) for 2-D NCS are obtained by using the expectation to process the Lyapunov function difference, so as to better study the transient performance of the systems. According to the recursive formula, an active compensation scheme for time delays of NPC is proposed, which takes into account quantization errors, packet losses, nonlinearity and interferences. Introducing FRS and FRB into 2-D NCS and considering the above factors in NPC scheme are new attempts made in this paper. An example is used to demonstrate the validity of the conclusions in the end.

Stability robust for fractional generalized multi-dimensional state–space models

In this work, we consider a new class of generalized fractional linear multidimensional state–space systems described by the Roesser model. We discuss a novel technique for analysing robust stability, focusing specifically on the stability of the closed-loop system in terms of the H 2 and H ∞ norms. Both discrete-time and continuous-time cases are addressed across various regions of the complex plane. An extension of the bounded real lemma is proposed, dealing with both continuous and discrete cases. This lemma is used to provide sufficient conditions, in the form of linear matrix inequalities, to ensure stability margin for the perturbed system. Motivating examples are presented to demonstrate the effectiveness of our main results.

Necessary optimality conditions for a Lagrange problem governed by a continuous Roesser model with Caputo derivatives

In the paper, we consider a Lagrange problem governed by a continuous Roesser type system with single partial Caputo derivatives. The necessary optimality conditions for such a problem are derived. In our approach, the increment method, as well as a fractional version of Gronwall’s type lemma for functions of two variables are used.

Event-triggered control of switched 2D continuous-discrete systems

This paper is concerned with the event-triggered control of switched two-dimensional (2D) continuous-discrete systems in Roesser model. A more general event-triggered scheme is proposed to reduce unnecessary resource waste and data redundancy, where a weighing coefficient and multiple parameter matrices are used. Based on the proposed event-triggered mechanism, a state feedback controller and a state-dependent switching signal are proposed. By using the multiple Lyapunov function method, sufficient conditions for the exponential stability of the closed-loop system are derived in terms of linear matrix inequalities. Finally, two examples are provided to illustrate the effectiveness of the proposed method.

Reachable set estimation for 2-D switched nonlinear positive systems with impulsive effects and bounded disturbances described by the Roesser model

<abstract><p>The reachable set estimation for two-dimensional (2-D) switched nonlinear positive systems (SNPSs) with bounded disturbances given by the Roesser model is investigated in this paper, in which both the time-varying delays and lagged impulsive effects are taken into account. By applying the average dwell time (ADT) technique, we provide a sufficient condition for the presence of a ball such that any solution of the system converges exponentially within it. An accurate estimate of the convergence rate is provided. We also extend the result to 2-D SNPSs with multi-directional delays, general 2-D switched linear systems, and 2-D SPNSs with heterogeneous delays. Finally, an example is worked out to demonstrate the effectiveness of the main result.</p></abstract>

A novel unbiased [formula omitted] filter design for 2-D Markov jump systems in the Roesser model with general transition probabilities

The paper delves into the intricate details of unbiased H∞ filtering for 2-D Markov jump systems with general transition probabilities in the light of the Roesser model. In order to allow the Markov jump systems to better model practical engineering applications, general transition probabilities are introduced. These probabilities are more flexible, encompassing all unknown, all known, and partially unknown cases to improve their practical applicability. The goal of this study is to showcase a novel unbiased filter to make the filtering error system mean-square asymptotically stable and meet a specified H∞ disturbance attenuation performance. By constructing the Lyapunov function, sufficient condition for the corresponding filter to exist and the solutions of its parameters are given through linear matrix inequalities. Eventually, the Darboux equation is used to prove the utility of the presented filter.

Dissipativity-Based Event-Triggered Sliding Mode Control of Discrete-Time 2-D Systems

This paper focuses on dissipativity analysis and dissipativity-based sliding mode control (SMC) of discrete-time two-dimensional (2-D) systems described by Roesser model. First, dissipativity is introduced for 2-D systems. Aimed at the characteristics of Roesser model, the horizontal and vertical sliding surface functions are constructed for the addressed 2-D systems, respectively. Then sufficient conditions are proposed to guarantee the asymptotic stability and the pre-specified dissipativity for the resultant reduced-order 2-D sliding mode dynamics. Next, the SMC law is developed such that the system trajectories are driven into the quasi-sliding mode band in a finite region and maintained there all the time. In order to achieve a better resource utilisation, the event-triggered strategy is further incorporated in the design of SMC law. The event-triggered rule is also established to implement the event-triggered SMC scheme for 2-D systems. In the meantime, the corresponding quasi-sliding mode band is obtained. Finally, one verification example is given to show the effectiveness of the proposed SMC design method.

Asynchronous Control of 2-D Semi-Markov Jump Systems Under Actuator Saturation

This brief investigates the asynchronous control issue of two-dimensional (2-D) semi-Markov jump systems in Roesser model. The switch of subsystems is governed by a novel mode generation approach, where the index of system mode is determined by the sum of variables of two directions. Such an approach can remove the problem of mode ambiguousness effectively. The actuator saturation and inaccessible system mode are simultaneously taken into account in the design of an asynchronous controller. The conditions are established to guarantee the almost surely exponential stability of the system. Additionally, estimation of the region of attraction is obtained by solving an optimization problem related to linear matrix inequalities. Finally, a numerical example is studied to demonstrate the availability of the designed asynchronous controller.