Discrete State-delayed Systems Research Articles

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

Reduced-order modeling methods via bivariate discrete orthogonal polynomials for two-dimensional discrete state-delayed systems

Reduced-order modeling methods via bivariate discrete orthogonal polynomials for two-dimensional discrete state-delayed systems

Robust <i>H<SUB align="right">∞</i> control for uncertain 2D state-delayed systems in the second FM model

This paper investigates the problem of robust H∞ control for two-dimensional (2D) discrete state delay systems described by the Fornasini-Marchesini (FM) second model. The parameter uncertainties are supposed to be norm-bounded. Our attention is focused on designing H∞ state feedback controllers guaranteeing the asymptotic stability and H∞ performance of the corresponding closed-loop system. A sufficient condition for H∞ disturbance attenuation performance for the nominal 2D discrete state delay system is first obtained. Next, a stabilising state feedback controller is designed such that the resulting closed-loop system is asymptotically stable and achieves a prescribed H∞ disturbance attenuation level. Furthermore, the resulting criteria are extended to robust H∞ control of the uncertain 2D state-delay system. Two examples are given to demonstrate the advantages of the proposed methods.

An LMI approach to design robust <i>H</i><SUB align="right">∞ controller for 2-D systems with delays

This paper focuses on H∞ controller design for two-dimensional (2-D) discrete state delay systems described by the second Fornasini-Marchesini local state space (FM LSS) model with polytopic uncertainties. The objective is to design a robust state feedback controller such that the corresponding closed-loop system achieves robust asymptotic stability and guarantees a prescribed H∞ performance index for all admissible uncertainties. Based on parameter-dependent Lyapunov functions and Finsler's lemma, a new sufficient condition for H∞ performance analysis of 2-D discrete systems with delays is developed. Then a stabilising state feedback controller is designed. A simulation example is exploited to show the effectiveness of the proposed approach.

Robust $$H_{\infty }$$ H ∞ control for 2-D discrete state delayed systems with polytopic uncertainties

This paper is concerned with the problem of robust $$H_{\infty }$$ control for two-dimensional (2-D) discrete state delay systems described by the Roesser model, the uncertain parameters are supposed to belong to a given convex bounded polyhedral domain. Both $$H_{\infty }$$ performance analysis and $$H_{\infty }$$ controller design are considered. Firstly, a sufficient condition for $$H_{\infty }$$ disturbance attenuation performance of the uncertain 2-D discrete systems with state delay is developed. Next, a stabilizing state feedback controller is designed such that the resulting closed-loop system is robustly asymptotically stable and has a prescribed level $$\gamma $$ of $$H_{\infty }$$ performance. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.

Optimal guaranteed cost control of uncertain 2-D discrete state-delayed systems described by the Roesser model via memory state feedback

This paper is concerned with the problem of optimal guaranteed cost control via memory state feedback for a class of uncertain two-dimensional (2-D) discrete state-delayed systems described by the Roesser model with norm-bounded uncertainties. A linear matrix inequality (LMI)-based sufficient condition for the existence of memory state feedback guaranteed cost controllers is established and a parameterized representation of such controllers (if they exist) is given in terms of feasible solutions to a certain LMI. Furthermore, a convex optimization problem with LMI constraints is formulated to select the optimal guaranteed cost controllers that minimize the upper bound of the closed-loop cost function. The proposed method yields better results in terms of least upper bound of the closed-loop cost function as compared with a previously reported result.

Robust Stabilization of Uncertain 2-D Discrete Delayed Systems

This paper is concerned with the stabilization of a class of two-dimensional discrete state-delayed systems described by the Fornasini–Marchesini second local state-space model subject to polytopic uncertainties. A delay-dependent stability criterion is derived for the existence of a memoryless state feedback controller such that the closed-loop system is robustly stable. To match practical issues the influence of finite wordlength nonlinearities in control implementation, delays and parameter uncertainties belonging to a known convex polytope are also discussed. The presented criteria are obtained by employing parameter-dependent Lyapunov–Krasovskii function and slack variables that augments the searching space allowing less conservative solutions. Finally, examples are provided to show the effectiveness of the proposal.

An Improved Criterion for the Global Asymptotic Stability of 2-D Discrete State-Delayed Systems with Saturation Nonlinearities

This paper investigates the global asymptotic stability of two-dimensional discrete state-delayed systems described by the Fornasini-Marchesini second local state-space model employing saturation nonlinearities. The structural properties of the multiple saturation nonlinearities in a greater detail are taken into account. Consequently, an improved delay-dependent stability criterion is obtained which is expressed in terms of linear matrix inequalities. The criterion is compared with a previously reported criterion. Finally, numerical examples are given to illustrate the usefulness of the proposed result.

Delay-Dependent Robust <i>H</i><sub>∞</sub> Control for Uncertain 2-D Discrete State Delay Systems Described by the General Model

This paper considers the problem of delay-dependent robust optimal H∞ control for a class of uncertain two-dimensional (2-D) discrete state delay systems described by the general model (GM). The parameter uncertainties are assumed to be norm-bounded. A linear matrix inequality (LMI)-based sufficient condition for the existence of delay-dependent g-suboptimal state feedback robust H∞ controllers which guarantees not only the asymptotic stability of the closed-loop system, but also the H∞ noise attenuation g over all admissible parameter uncertainties is established. Furthermore, a convex optimization problem is formulated to design a delay-dependent state feedback robust optimal H∞ controller which minimizes the H∞ noise attenuation g of the closed-loop system. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.

Robust Optimal H<sub>∞</sub> Control for Uncertain 2-D Discrete State-Delayed Systems Described by the General Model

This paper investigates the problem of robust optimal H∞ control for uncertain two-dimensional (2-D) discrete state-delayed systems described by the general model (GM) with norm-bounded uncertainties. A sufficient condition for the existence of g-suboptimal robust H∞ state feedback controllers is established, based on linear matrix inequality (LMI) approach. Moreover, a convex optimization problem is developed to design a robust optimal state feedback controller which minimizes the H∞ noise attenuation level of the resulting closed-loop system. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed method.

Non-fragile robust optimal guaranteed cost control of uncertain 2-D discrete state-delayed systems

ABSTRACTThis paper is concerned with the problem of non-fragile robust optimal guaranteed cost control for a class of uncertain two-dimensional (2-D) discrete state-delayed systems described by the general model with norm-bounded uncertainties. Our attention is focused on the design of non-fragile state feedback controllers such that the resulting closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible parameter uncertainties and controller gain variations. A sufficient condition for the existence of such controllers is established under the linear matrix inequality framework. Moreover, a convex optimisation problem is proposed to select a non-fragile robust optimal guaranteed cost controller stabilising the 2-D discrete state-delayed system as well as achieving the least guaranteed cost for the resulting closed-loop system. The proposed method is compared with the previously reported criterion. Finally, illustrative examples are given to show the potential of the proposed technique.

Delay-dependent [formula omitted] control for 2-D switched delay systems in the second FM model

This paper is concerned with the problem of delay-dependent H∞ control for 2-D (two-dimensional) switched discrete state delay systems described by the second FM (Fornasini and Marchesini) state-space model. Firstly, some sufficient conditions for the exponential stability and weighted H∞ disturbance attenuation performance of the underlying system are derived via the average dwell time approach. Then, based on the obtained results, a state feedback controller design is proposed to guarantee that the resulting closed-loop system is exponentially stable and achieves a prescribed disturbance attenuation level γ. Finally, a numerical example is provided to verify the effectiveness of the proposed method.

An LMI based criterion for the global asymptotic stability of 2-D discrete state-delayed systems with saturation nonlinearities

This paper deals with the problem of global asymptotic stability of a class of two-dimensional (2-D) discrete systems described by the Fornasini–Marchesini second local state-space (FMSLSS) model in presence of saturation nonlinearities and state delays in each of the two independent directions of information propagation. A linear matrix inequality (LMI) based criterion for the global asymptotic stability of such systems is presented. It is shown that several previously reported stability criteria for 2-D discrete FMSLSS model with saturation nonlinearities are recovered from the presented approach as special cases.

LMI-Based Criterion for the Robust Stability of 2D Discrete State-Delayed Systems Using Generalized Overflow Nonlinearities

This paper addresses the problem of global asymptotic stability of a class of discrete uncertain state-delayed systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model using generalized overflow nonlinearities. The uncertainties are assumed to be norm bounded. A computationally tractable, that is, linear-matrix-inequality-(LMI-) based new criterion for the global asymptotic stability of such system is proposed. It is demonstrated that several previously reported stability criteria for two-dimensional (2D) systems are recovered from the presented approach as special cases. Numerical examples are given to illustrate the usefulness of the presented approach.

Delay-dependent H ∞ control for 2-D discrete state delay systems in the second FM model

This paper is concerned with the problem of delay-dependent H ∞ control for two-dimensional (2-D) discrete state delay systems described by the second Fornasini and Marchesini (FM) state-space model. Based on a summation inequality, a sufficient condition to have a delay-dependent H ∞ noise attenuation for this 2-D system is given in terms of linear matrix inequalities (LMIs). A delay-dependent optimal state feedback H ∞ controller is obtained by solving an LMI optimization problem. Finally, a simulation example of thermal processes is given to illustrate the effectiveness of the proposed result.

H ∞ filtering of 2-D discrete state-delayed systems

In this paper, we deal with delay-independent and delay-dependent H ? filtering problems for a class of two-dimensional (2-D) discrete time-invariant systems with state delays. The 2-D systems are described by local state-space (LSS) Fornasini---Marchesini (FM) second model. First, delay-dependent bounded real lemma is proposed through introducing free weighting matrices. Then the delay-independent and delay-dependent H ? filtering designs are developed to assure the stability and H ? performance ? of filtering error systems via LMIs' feasibility. Furthermore, the minimum H ? norm bound ? can be obtained by solving linear convex optimization problems. Numerical examples demonstrate the effectiveness and advantages of our results.

H∞ Control for 2-D Discrete State Delayed Systems in the Second FM Model

This paper is concerned with the problem of H ∞ control for two-dimensional (2-D) discrete state delay systems described by the second Fornasini and Marchesini (FM) state-space model. A sufficient condition to have an H ∞ noise attenuation for this 2-D system is given in terms of a certain linear matrix inequality (LMI). The optimal H ∞ controller is obtained by solving a convex optimization problem. Finally, a simulation example is given to illustrate the effectiveness of the proposed result.

Hamiltonian (script capital H)]∞ mode reduction for two-dimensional discrete state-delayed systems

The problem of ℋ∞ model reduction for two-dimensional (2-D) discrete systems with delay in state is considered. The mathematical model of 2-D systems is established on the basis of the well-known Fornasini–Marchesini local state-space. First, conditions are established to guarantee the asymptotic stability and a prescribed noise attenuation level in the ℋ∞ sense for the underlying system. For a given stable system, attention is focused on the construction of a reduced-order model, which approximates the original system well in an ℋ∞ norm sense. Sufficient conditions are proposed for the existence of admissible reduced-order solutions. Since these obtained conditions are not expressed as strict linear matrix inequalities (LMIs), the cone complementary linearisation method is exploited to cast them into sequential minimisation problems subject to LMI constraints, which can be readily solved using standard numerical software. These obtained results are further extended to more general cases whose system states contain multiple delays. Two numerical examples are provided to demonstrate the effectiveness of the proposed techniques.

Robust [formula omitted] control for a class of uncertain nonlinear two-dimensional systems with state delays

This paper considers the problem of robust H ∞ control for uncertain 2-D discrete state-delayed systems in the Fornasini–Marchesini second local state-space model with a class of generalized Lipschitz nonlinearities. The parameter uncertainty is assumed to be norm-bounded. The problem to be addressed is the design of state feedback controllers such that the stability of the resulting closed-loop system is guaranteed and a prescribed H ∞ performance level is ensured for all admissible uncertainties. In terms of a linear matrix inequality (LMI), a sufficient condition for the solvability of the problem is obtained. A desired state feedback controller can be constructed by solving a certain LMI. A numerical example is provided to demonstrate the application of the proposed method.

Robust stability and stabilisation of 2D discrete state-delayed systems

In this paper, we first present sufficient stability and robust stability conditions for discrete linear state-delayed 2D systems in terms of linear matrix inequalities. All results are obtained with Fornasini–Marchesini delay model but appropriate transformation to the corresponding Roesser form is provided as well. Generalisation to the multiple state-delayed case is also given. Then the stabilisation and robust stabilisation using static state feedback are studied. Stabilising feedback gain matrices are constructed based on the solutions of certain linear matrix inequalities. An numerical example is used to illustrate the effectiveness of the approach.