Memory State Feedback Research Articles

An Improved Memory State Feedback RMPC for Uncertain Constrained Linear Systems with Multiple Uncertain Delays

The problem of robust asymptotic stabilization is considered for a class of discrete-time uncertain linear systems with multiple uncertain time-delayed states and input constraints. Compared with other works in the literature, the proposed approach takes the information of the delayed states with the estimated time-delays indices into full consideration. Based on the predictive control principle of receding horizon optimization and Lyapunov stability theory combined with linear matrix inequalities (LMIs) techniques, a time-delayed state dependent quadratic function is considered for incorporating MPC problem formulation. The robust MPC problem is formulated to minimize the upper bound of infinite horizon cost that satisfies the sufficient conditions. The proposed approach allows for the synthesis of robust memory state feedback controllers with respect to uncertainties on the implemented delay. Since developing the improved memory state feedback controller, the novel improved method is much less conservative and more general. Finally, the numerical simulation results prove availability of the proposed method.

Periodically time-varying memory static output feedback control design for discrete-time LTI systems

This paper addresses the problem of static output feedback (SOF) stabilization for discrete-time LTI systems. We approach this problem using the recently developed periodically time-varying memory state-feedback controller (PTVMSFC) design scheme. A bilinear matrix inequality (BMI) condition which uses a pre-designed PTVMSFC is developed to design the periodically time-varying memory SOF controller (PTVMSOFC). The BMI condition can be solved by using BMI solvers. Alternatively, we can apply two-steps and iterative linear matrix inequality algorithms that alternate between the PTVMSFC and PTVMSOFC designs. Finally, an example is given to illustrate the proposed methods.

Extended finite-time H∞ control for uncertain switched linear neutral systems with time-varying delays

This paper is concerned with the finite-time H∞ control problem for a class of uncertain switched linear neutral systems with time-varying delays. By fully exploiting the mode-dependency of the proposed Lyapunov–Krasovskii functionals, the considered systems could be further investigated with stable and unstable subsystems being concurrently contained. Sufficient criteria are first derived for ensuring finite-time boundedness of the underlying system with a given maximum ratio of activation time between unstable subsystems and stable ones. Then the H∞ performance analysis and the memory state-feedback controller design are carried out for a given performance index. Finally, two numerical examples are presented to illustrate the potential and advantages of the developed findings.

Formula omitted] tracking of uncertain stochastic time-delay systems: Memory state-feedback controller design

The problem of state robust H∞ tracking control for uncertain stochastic systems with interval time-varying delay is considered in this paper. The target is to design a memory state feedback controller such that the resulting closed-loop augmented system is robustly stochastically asymptotically stable and the states of original systems can follow the reference signal with given H∞ performance. Firstly, by constructing delay-partitioning-dependent Lyapunov–Krasovskii functional with reciprocally convex approach, a delay-dependent condition guaranteeing the robust H∞ tracking performance is proposed in a set of matrix inequalities. Secondly, new stability criteria for stochastic systems with time-varying delay are given with less conservativeness than some recent results. Thirdly, memory state feedback controller is designed via a set of linear matrix inequalities (LMIs) which can be solved by Matlab LMI toolbox. At last, numerical simulations are addressed to show the effectiveness of the proposed methods.

Finite-time H∞ control for a class of nonlinear system with time-varying delay

This paper is concerned with the finite-time H ∞ control for a class of nonlinear system with time-varying delay, which can be represented by Takagi–Sugeno (T–S) fuzzy system. First, a new integral inequality, which is less conservative than other existing ones, is established by introducing some free fuzzy weighting matrices. Based on a new fuzzy Lyapunov–Krasovskii function, delay-dependent finite-time boundedness (FTB) criterion and H ∞ finite-time boundedness ( H ∞ FTB) criterion are derived for the open-loop fuzzy time-delay system. Then, some delay-dependent finite-time stabilization conditions are given by designing a memory state feedback controller, which is based on the so-called parallel distributed compensation (PDC) scheme. Finally, an example is provided to illustrate the validity of the proposed design approach.

Further results on memory control of nonlinear discrete-time networked control systems with random input delay

This paper is concerned with the problem of memory state feedback stabilization for a class of nonlinear discrete-time networked control systems with partly known probability distribution of input delay. Different from the common assumptions on the delay in the existing literatures, it is assumed that the probabilities of the delay taking values in a finite set are partly known or fully known in advance. In terms of the information about the occurrence probabilities of the delay taking values in the two finite sets, a new stochastic delay model is proposed, where the probability information of the delay is included in the parameter matrices of the transformed system. Based on the new model, a delay-dependent stabilization criterion is derived using a combination of the Lyapunov functional method, convexity of matrix inequalities, and linear matrix inequality technique. Finally, three illustrative examples are provided to show the effectiveness and applicability of the developed theoretical results.

Memory State Feedback RMPC for Multiple Time-Delayed Uncertain Linear Systems with Input Constraints

This paper focuses on the problem of asymptotic stabilization for a class of discrete-time multiple time-delayed uncertain linear systems with input constraints. Then, based on the predictive control principle of receding horizon optimization, a delayed state dependent quadratic function is considered for incorporating MPC problem formulation. By developing a memory state feedback controller, the information of the delayed plant states can be taken into full consideration. The MPC problem is formulated to minimize the upper bound of infinite horizon cost that satisfies the sufficient conditions. Then, based on the Lyapunov-Krasovskii function, a delay-dependent sufficient condition in terms of linear matrix inequality (LMI) can be derived to design a robust MPC algorithm. Finally, the digital simulation results prove availability of the proposed method.

A Guaranteed Cost Control for Stochastic Distribution System with Time-delay

This article investigates the guaranteed cost control problem for the stochastic distribution system with time-delay. Attention is focused on a memory state feedback control law based on Linear Matrix Inequality (LMI) with model transformation such that the closed-loop system is asymptotically stable and the guaranteed cost index is not more than a specied upper bound, which ensure that the system output Probability Density Function (PDF) follows the target probability density function. A comparative study of an example problem has show to illustrate the proposed method.

Robust H∞ guaranteed cost control for uncertain switched descriptor delayed systems with nonlinear disturbance

This article considers the issues of robust [Formula: see text] guaranteed cost control and memory state feedback stabilization for a class of uncertain switched descriptor delayed systems with nonlinear disturbance. Sufficient conditions for the existences of robust [Formula: see text] guaranteed cost controller in terms of linear matrix inequalities and switching strategy are proposed based on generalized Lyapunov function and convex optimization approach, and the memory state feedback controller ensures that the closed-loop systems satisfy the guaranteed cost function with a prescribed [Formula: see text][Formula: see text]-disturbance attenuation. Moreover, a convex optimization problem with linear matrix inequality constraints is formulated and solved by mean of the linear matrix inequality toolbox, and the optimal [Formula: see text] guaranteed cost memory state feedback controller with an upper bound of cost function is obtained. Finally, a numerical example illustrates the effectiveness of the proposed method.

Memory State-Feedback Stabilization for a Class of Time-Delay Systems with a Type of Adaptive Strategy

Stabilization of a class of systems with time delay is studied using adaptive control. With the help of the “error to error” technique and the separated “descriptor form” technique, the memory state-feedback controller is designed. The adaptive controller designed can guarantee asymptotical stability of the closed-loop system via a suitable Lyapunov-Krasovskii functional. Some sufficient conditions are derived for the stabilization together with the linear matrix inequality (LMI) design approach. Finally, the effectiveness of the proposed control design methodology is demonstrated in numerical simulations.

Optimal guaranteed cost control of uncertain 2D discrete systems with both shift delays and input delays via memory state feedback

The problem of optimal guaranteed cost control for a class of 2D discrete uncertain systems under shift delays and input delays in a Fornasini–Marchesini (FM) second model setting via memory state feedback is considered in this paper. A linear matrix inequality (LMI)-based criterion for the existence of guaranteed cost controllers is established. Furthermore, a convex optimization problem with LMI constraints is formulated to design the optimal guaranteed cost controllers that minimize the upper bound of the closed-loop cost function. Illustrative examples are given to demonstrate the applicability of the proposed method.

Periodically Time-Varying Memory State-Feedback for RobustH2Control of Uncertain Discrete-Time Linear Systems

This study is concerned with the synthesis of periodically time-varying memory state-feedback controllers (PTVMSFCs) for discrete-time linear systems. In our preceding studies, we have already established a solid theoretical basis for linear matrix inequality (LMI)-based (robust) H ∞-PTVMSFCs synthesis, and the goal of this paper is to extend those results to the H 2 performance criterion. In the H 2 case, the main difficulty stems from the fact that we have to ensure the existence of common auxiliary variables for multiple LMI conditions that are related to the Lyapunov inequality and the inequalities for bounding traces that characterize the H 2 norm. We can overcome this difficulty and derive a necessary and sufficient LMI condition for the optimal H 2-PTVMSFC synthesis. On the basis of this result, we also consider robust H 2-PTVMSFC synthesis for LTI systems with parametric uncertainties.

An LMI Approach to Optimal Guaranteed Cost Control of Uncertain 2-D Discrete Shift-Delayed Systems via Memory State Feedback

This paper deals with the problem of optimal guaranteed cost control via memory state feedback for a class of two-dimensional (2-D) discrete shift-delayed systems in Fornasini–Marchesini (FM) second model with norm-bounded uncertainties. A new criterion for the existence of memory state feedback guaranteed cost controllers is derived, based on the linear matrix inequality (LMI) approach. Moreover, a convex optimization problem with LMI constraints is formulated to design the optimal guaranteed cost controllers which minimize the upper bound of the closed-loop cost function. Illustrative examples demonstrate the merit of the proposed method in the aspect of conservativeness over a previously reported result.

Delay-dependent observer-based [formula omitted] finite-time control for switched systems with time-varying delay

This paper is concerned with the problem of observer design for switched linear systems with time-varying delay and exogenous disturbances. The attention is focused on designing the full-order observers that guarantee the finite-time bounded and H∞ finite-time stability of the dynamic augmented system. Based on linear matrix inequalities (LMIs) technology and an average dwell time (ADT) approach, sufficient conditions which ensure the observer-based finite-time bounded and H∞ finite-time stability are given, respectively. By using a state observer, the memory state feedback controller is designed to finite-time stabilize a time-delay switched system, and the conditions are formulated in terms of delay-dependent LMIs. An example is given to illustrate the efficiency of the proposed methods.

Robust Stabilization for Stochastic Systems with Time‐Delay and Nonlinear Uncertainties

This paper deals with the problem of robust stabilization of stochastic systems with time‐delay and nonlinear uncertainties via memory state feedback. Based on Lyapunov krasoviskii functional, some sufficient conditions on local (global) stabilization are given in terms of matrix inequalities. In particular, these stabilizable conditions for a class of nonlinear stochastic time‐delay systems are derived in the form of linear matrix inequalities, which have the advantage of easy computation. Moreover, the corresponding results are further extended to the stochastic multiple time‐delays systems. Finally, an example is presented to show the superiority of memory state feedback controller to memoryless state feedback controller.

Stabilization of jump linear systems with mode‐dependent time‐varying delays

AbstractThis paper deals with the stabilization problems for a class of Markovian jump systems with time delays which are time varying and depending on system mode. Following the recent study on the class of systems, improved sufficient condition for stochastic stability of the underlying systems is derived by constructing a different Lyapunov–Krasovskii functional. Basing on this new criterion, a stabilization algorithm through memory state feedback controller is designed. Illustrative numerical examples are provided to demonstrate the effectiveness of the proposed approaches. Copyright © 2010 John Wiley & Sons, Ltd.

Periodically time-varying memory state-feedback controller synthesis for discrete-time linear systems

In this paper, we deal with discrete-time linear periodic/time-invariant systems with polytopic-type uncertainties and propose a new linear matrix inequality (LMI)-based method for robust state-feedback controller synthesis. In stark contrast with existing approaches that are confined to memoryless static controller synthesis, we explore dynamical controller synthesis and reveal a particular periodically time-varying memory state-feedback controller (PTVMSFC) structure that allows LMI-based synthesis. In the context of robust controller synthesis, we prove rigorously that the proposed design method encompasses the well-known extended-LMI-based static controller synthesis methods as particular cases. Through numerical experiments, we demonstrate that the suggested design method is indeed effective in achieving less conservative results, under both periodic and time-invariant settings. We finally derive a viable test to verify that the designed robust PTVMSFC is “exact” in the sense that it attains the best achievable robust performance. This exactness verification test works fine in practice, and we will show via a numerical example that exact robust control is indeed attained by designing PTVMSFCs, even for such a problem where the standard memoryless static state-feedback fails.

On designing memory state feedback controller for linear systems with interval time-varying delay

This paper is concerned with the design of a memory state feedback controller for linear systems with interval time-varying delays. The time delay is assumed to be a time-varying continuous function belonging to a given interval, which means that the lower and upper bounds of time-varying delay are available. First, a less conservative delay-range-dependent stability criteria is proposed by using a new interval fraction method. In the process of controller synthesis, the history information of system is considered in the controller design by introducing the lower delay state. Moreover, the usual memoryless state feedback controller for the underlying systems could be considered as a special case of the memory case. Finally, two numerical examples are given to show the effectiveness of the proposed method.

Robust memory state feedback model predictive control for discrete-time uncertain state delayed systems

In this paper, we propose a memory state feedback model predictive control (MPC) law for a discrete-time uncertain state delayed system with input constraints. The model uncertainty is assumed to be polytopic, and the delay is assumed to be unknown, but with a known upper bound. We derive a sufficient condition for cost monotonicity in terms of LMI, which can be easily solved by an efficient convex optimization algorithm. A delayed state dependent quadratic function with an estimated delay index is considered for incorporating MPC problem formulation. The MPC problem is formulated to minimize the upper bound of infinite horizon cost that satisfies the sufficient conditions. Therefore, a less conservative sufficient conditions in terms of linear matrix inequality (LMI) can be derived to design a more robust MPC algorithm. A numerical example is included to illustrate the effectiveness of the proposed method.

Memory state feedback controller design for singular systems with multiple internal constant point delays

The problem of delay-dependent stabilisation for singular linear continuous-time systems with multiple internal incommensurate constant point delays is investigated. The condition when a singular system subject to point delays is regular independent of time delays is given and it can be easily tested with numerical or algebraic methods. Based on the Lyapunov-Krasovskii functional approach and the descriptor integral-inequality lemma, a sufficient condition for delay-dependent stability is obtained. The main idea is to design multiple memory state feedback control laws such that the resulting closed-loop system is regular independent of time delays, impulse free and stable via solving matrix inequality problem. An explicit expression for the desired memory state feedback control law is also given. Finally, a numerical example is presented to illustrate the effectiveness and the availability for the proposed method.