Linear Matrix Inequality Method Research Articles

Non-fragile ${H_\infty }$ filter design for uncertain neutral Markovian jump systems with time-varying delays

<abstract> <p>This paper deals with the problem of non-fragile ${H_\infty }$ filter design for a class of neutral Markovian jump systems with parameter uncertainties and time-varying delays. The parameter uncertainties are norm-bounded, and time-varying delays include state and neutral time-varying delays. First, by selecting the appropriate stochastic Lyapunov-Krasovskii functional and using the integral inequality technique, sufficient conditions are obtained to make the filtering error system not only stochastically stabilized, but also mode and delay dependent. Second, by the utilizing linear matrix inequality method, sufficient conditions are obtained for the filtering error system to be stochastically stable and to have a prescribed ${H_\infty }$ performance level $\gamma $. Based on this result, by processing the uncertainty terms, sufficient conditions for the existence of the filter are obtained, and mode-dependent filter parameters are given. Finally, by numerical simulation, the feasibility and validity of the theoretical results are verified.</p> </abstract>

Asynchronous finite‐time dynamic output feedback control for discrete‐time switched linear systems with admissible edge‐dependent average dwell time

AbstractThis paper is concerned with the problem of asynchronous finite‐time dynamic output feedback (DOF) control for a class of discrete‐time switched linear systems under the admissible edge‐dependent average dwell time (AED‐ADT) switching scheme. The main goal of the paper is to design a DOF controller to ensure that the resulting closed‐loop system is finite‐time bounded with AED‐ADT switching and has a specific performance. Firstly, some new sufficient conditions for stability criterion and performance analysis are established based on the multiple Lyapunov functionals technique and the linear matrix inequalities method. Secondly, a type of DOF controllers that guarantee that the closed‐loop system has desired performance is designed. Finally, the effectiveness of the proposed approaches is elaborated with a numerical example.

Optimal Control of Hybrid Photovoltaic/Thermal Water System in Solar Panels Using the Linear Parameter Varying Approach

During photovoltaic (PV) conversion in solar panels, a part of the solar radiation is not converted to electricity by the cells, producing heat that could increase their temperature. This increase in temperature deteriorates the performance of the PV panel. In this paper, a hybrid PV/thermal (PV/T) water system is proposed to mitigate this problem. This system combines a PV panel and a thermal collector. In this paper, we focused on the modeling and control of this hybrid system in the linear parameter varying (LPV) framework. An optimal linear quadratic regulator (LQR) is proposed to control the PV cell temperature around an optimal value that maximises electricity generation. Since the system model is nonlinear, an optimal LQR gain-scheduling state-feedback control approach based on an LPV representation of the nonlinear model is designed using the Linear Matrix Inequality (LMI) method. The goal is to obtain the maximum electrical power for each solar panel. Since a reduced number of sensors is available, an LPV Kalman filter is also proposed to estimate the system states required by the state-feedback controller. The obtained results in a laboratory setup in simulation are used to assess the proposed approach, showing promise in terms of control performance of the PV/T system.

Novel adaptive filter design for complex‐valued network systems under hybrid cyber attacks

AbstractThis paper is concerned with the problem of designing adaptive event‐triggered filter for complex‐valued network system under complex‐valued hybrid cyber attack. Firstly, the main contribution of the article is to propose a complex‐valued adaptive event triggered strategy to improve the resource utilisation in the network channel. Secondly, during the modeling process of the filtering error model, we introduce complex‐valued stochastic deception attacks and replay attacks that follow the Bernoulli distribution, thereby forming the complex‐valued hybrid network attacks investigated in this paper. Sufficient conditions for the asymptotic stability of the designed complex‐valued filtered error system are derived using Lyapunov stability theory. In addition, the parameters of the filter are derived using the linear matrix inequality (LMI) method. Finally, a numerical simulation example is given to verify the feasibility of the proposed method.

Optimal oxygen excess ratio tracking of proton exchange membrane fuel cell with uncertainty based on robust model predictive control strategy

AbstractTo address the challenge of tracking the optimal oxygen excess ratio (OER) in the cell stack cathode of the proton exchange membrane fuel cell (PEMFC), which is subject to norm‐bounded parameter uncertainty and frequent external perturbations, this manuscript provides a novel robust model predictive control strategy with a state feedback control structure and hard constraints. We aim to minimize the tracking error of OER while maximizing the net power under varying operational conditions of the PEMFC. Initially, a control‐oriented model for the air supply system is built and its accuracy is validated by comparing it with experimental results. Next, we construct the discrete state‐space equations for optimal control and employ the linear matrix inequality (LMI) method to transform the problem of difficult min‐max optimization solutions into a convex optimization problem with LMI constraints. Finally, the effectiveness of the proposed control algorithm is validated through simulation. The results demonstrate the strong robustness and superiority of the proposed controller against uncertainties in plant parameters for robust OER trajectory tracking. It improves the transient performance through robust precision tracking applications, which will eventually accelerate PEMFC commercialization.

Robust output regulation of a class of smart actuators described by a minimum phase LPV dynamics

This paper presents a new control strategy for a class of minimum phase linear parameter-varying (LPV) systems representative of smart material actuators. In position control applications of such devices, one is typically interested in achieving output regulation with an arbitrary exponential decay rate. In principle, this problem can be tackled by assigning an exponential decay rate to the full system state, by means of well-established linear matrix inequalities (LMI) methods. For the class of systems under investigation, however, this approach leads to excessively large controller gains in case the desired decay rate is faster than the open-loop zero dynamics. In addition, the existence of unmeasurable state variables related to the material microstructure makes it not possible to directly implement full state feedback laws which are commonly adopted in LPV theory. To overcome these issues, a new design strategy is proposed. The key idea relies on arbitrarily shaping the output exponential decay rate without requiring fast convergence of the full state vector. This goal is achieved by means of a partial state feedback control law which solely depends on the measurable system states. A LMI algorithm is also developed to systematically address the design of the partial state feedback controller. The method is validated by means of simulations on generic examples, as well as via experiments on a mechatronic positioning system based on a dielectric elastomer membrane. In case the desired output convergence speed is faster than the open-loop zero dynamics, it is shown that the new approach leads to better transient behaviors and significantly smaller controller gains than standard LPV design techniques.

Event‐based reduced‐order H∞$H_{\infty }$ estimation for switched complex networks based on T‐S fuzzy model

AbstractThis paper investigates the design of a reduced‐order filter for a specific class of switched complex network systems with time‐varying delays. To handle the nonlinear components of the complex network, a T‐S fuzzy model is employed to convert them into a set of linear components. To tackle the issue of heavy network load, a memory‐based adaptive trigger mechanism is proposed. In this study, a reduced‐order state estimator is designed using the T‐S fuzzy model. To demonstrate the exponential stability of the error system, a suitable Lyapunov function is constructed based on the Lyapunov stability principle. The parameter matrix of the reduced‐order estimator is determined using the linear matrix inequality and convex linearization method. Additionally, a sufficient condition for the exponential stability of the error system at the suppression level is provided. Finally, the feasibility of the proposed scheme is validated through a simulation experiment.

Novel stability conditions for some generalization of Nicholson's blowflies model with stochastic perturbations

We consider a generalization of the well-known nonlinear Nicholson blowflies model with stochastic perturbations. Stability in probability of the positive equilibrium of the considered equation is studied. Two types of stability conditions: delay-dependent and delay-independent conditions are obtained, using the method of Lyapunov functionals and the method of linear matrix inequalities. The obtained results are illustrated by numerical simulations by means of some examples. The results are new, and complement the existing ones. doi: 10.1017/S1446181123000147

Non-fragile guaranteed cost control of microbial fuel cells

A microbial fuel cell (MFC), which is a new type of energy source, utilises electrogenic bacteria in sewage or soil to convert chemical energy into electrical energy. MFCs typically require an external controller to provide a stable output voltage to the external load. This study develops a non-fragile guaranteed cost (NFGC) controller to suppress the interference of the controller of an MFC and ensure that the quadratic cost function of the system satisfies certain performance indexes. First, for the convenience of controller design, a Takagi–Sugeno fuzzy model is established to approximate a single-chamber single-population MFC model. Subsequently, the linear matrix inequality method is used to design the NFGC controller. This control scheme can reduce the influence of controller disturbances on the system and ensure asymptotic stability of the closed-loop system under the specified upper bound of the provided cost function. The simulation results demonstrate that the developed control method has a shorter adjustment time and smaller steady-state error than traditional control methods such as sliding mode control (SMC), backstepping control, and fuzzy SMC

Robust dynamic output feedback predictive control for discrete uncertain systems with time-varying delays

A robust dynamic output feedback predictive control approach is developed for a discrete system with time-varying delays, unknown external disturbances, and unmeasurable states. First, the discrete system is transformed into an incremental state deviation model. Based on this model, a novel tracking deviation feedback model is established by extending the output tracking error. Then, a robust predictive control law, possessing more degrees of freedom, is designed. The closed-loop model is further given in conjunction with the feedback model. Second, by using the linear matrix inequality (LMI) method, relaxation technique, and variable transformation method, a less conservative stability condition is given in LMI form, which allows the controller to tolerate a greater range of time-varying delays. The gains of the control law are acquired by solving the stability condition, and the control performance can be significantly enhanced. Finally, by utilizing the TTS20 water tank as a simulation case, the viability and effectiveness of the proposed method are demonstrated.

Load frequency control of power system based on improved AFSA-PSO event-triggering scheme

Aiming at the impact of redundant information transmission on network resource utilization in current power systems, an improved event-triggered scheme based on particle swarm optimization and artificial fish swarm algorithm for power system load frequency control (LFC) with renewable energy is proposed. First of all, to keep the stability and security of power systems with renewable energy, the load frequency control scheme is investigated in this paper. Then, to relieve the communication burden and increase network utilization, an improved event-triggered scheme based on the particle swarm algorithm and artificial fish swarm algorithm is explored for the power system load frequency control. Then, by utilizing improved Lyapunov functional and the linear matrix inequality method, sufficient condition for the H∞ stability of the load frequency control system is established. Finally, a two-area load frequency control system and IEEE-39 node simulation models are constructed to verify the effectiveness and applicability of the proposed method.

Alternate Admissibility LMI Criteria for Descriptor Fractional Order Systems with 0 < α < 2

The paper focuses on the admissibility problem of descriptor fractional-order systems (DFOSs). The alternate admissibility criteria are addressed for DFOSs with order in (0,2) which involve a non-strict linear matrix inequality (LMI) method and a strict LMI method, respectively. The forms of non-strict and strict LMIs are brand new and distinguished with the existing literature, which fills the gaps of studies for admissibility. These necessary and sufficient conditions of admissibility are available to the order in (0,2) without separating the order ranges into (0,1) and [1,2). Based on the special position of singular matrix, the non-strict LMI criterion has an advantage in handling the DFOSs with uncertain derivative matrices. For the strict LMI form, a method involving least real decision variables is derived which is more convenient to process the practical solution. Three numerical examples are given to illustrate the validity of the proposed results.

Observer‐based security control for distributed cyber‐physical systems under replay attacks

AbstractThis paper considers the security control problem over a finite horizon for distributed cyber‐physical systems (CPSs) under replay attacks and switching topologies. A more reasonable attack model is established to describe the randomly occurring replay attacks, where the measurement information is maliciously replaced by previous unnecessary information. Under the Markovian switching communication network, a distributed observer‐based control protocol is developed to mitigate the influence on system performance resulting from disturbances and replay attacks. Then, by using recursive linear matrix inequality method and stochastic analysis technique, two sufficient conditions are derived to ensure the consensus of the closed‐loop system while satisfying the prescribed performance index. Gain matrices of observer and controller are derived by resorting to the matrices inequalities that are reality solvable. Finally, simulated examples are presented to compare the control performance under different attack strategies, and explore the relationship between the number of consecutive attacks and the performance index.

Set membership filtering for discrete saturated time‐varying networked systems with incomplete measurements under round‐robin protocol

AbstractIn this paper, the set membership filtering problem is investigated for a class of discrete networked systems with time delay and state saturation under the round‐robin (RR) protocol, where the system noise is unknown but bounded. In order to reduce the communication burden, the RR protocol is used to schedule the measurement information of the system. In addition, the incompleteness of the measurement information is considered. A set membership filter is established based on incomplete measurements. The objective is to give a criterion that the filtering error is confined to the ellipsoidal set by using the recursive linear matrix inequality (RLMI) method. Moreover, a convex optimization method is proposed to minimize the obtained ellipsoids. Finally, a numerical simulation illustrates that the designed set membership filtering scheme is effective.

Dynamic Output Feedback Quantization Control of a Networked Control System with Dual-Channel Data Packet Loss

In this paper, the design of a dynamic output feedback controller for a networked control system with dual-channel data packet loss and special discrete-time delay is studied, in which the data packet loss is described by the Markov process. In order to effectively alleviate the problem of network congestion, a quantizer was added to the sensor-to-controller channel. The transition probabilities of the Markov process are uncertain, but they exist in the convex sets of known convex polyhedron types. The mode-dependent Lyapunov function was constructed, and a sufficient condition was given to make the closed-loop system stochastically stable and satisfy the performance index. The parameters of the controller were solved by the linear matrix inequality method. Finally, an example of aircraft shows the validity of the proposed approach. A numerical example is compared with other literature, showing the superiority of the proposed approach.

Mean-Square Stability of Uncertain Delayed Stochastic Systems Driven by G-Brownian Motion

This paper investigates the mean-square stability of uncertain time-delay stochastic systems driven by G-Brownian motion, which are commonly referred to as G-SDDEs. To derive a new set of sufficient stability conditions, we employ the linear matrix inequality (LMI) method and construct a Lyapunov–Krasovskii function under the constraint of uncertainty bounds. The resulting sufficient condition does not require any specific assumptions on the G-function, making it more practical. Additionally, we provide numerical examples to demonstrate the validity and effectiveness of the proposed approach.

An ${H_\infty }$ Load Frequency Control Scheme for Multi-Area Power System Under Cyber-Attacks and Time-Varying Delays

In the power system, the application of the signals transmitted from the sensors to the controller can significantly improve the dynamic performance. However, cyber-attacks and time delays exist widely in the communication network, which has a considerable effect on stability, operation, and control. In this paper, an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\boldsymbol{H}}_\infty }$</tex-math></inline-formula> load frequency control (LFC) scheme for multi-area power systems under cyber-attacks and time-varying delays is investigated. First, false data injection attacks (FDIA), as well as denial of service (DoS) attacks, are viewed as two typical cyber-attacks and introduced into the multi-area power system. Then, the state-space equations of the LFC power system under these two attacks and time-varying delays are analyzed and modeled. Furthermore, by using Lyapunov stability theory and linear matrix inequality (LMI) method, an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\boldsymbol{H}}_\infty }$</tex-math></inline-formula> LFC scheme for attacked and delayed power systems is developed. The purpose of the proposed controller is to guarantee the closed-loop system exponentially mean-square stable with prescribed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\boldsymbol{H}}_\infty }$</tex-math></inline-formula> performance. Finally, a three-area LFC system is employed to demonstrate the effectiveness of the proposed mechanism. The simulation results verified that the control performance of an attacked and delayed system can be improved significantly via the designed controller.

High-precision controller using LMI method for three-axis flexible satellite attitude stabilisation

AbstractThis paper considers the problem of a three-axis flexible satellite attitude stabilisation subject to the vibration of flexible appendages and external environmental disturbances, which affect the rigid body motion. To solve this problem, a disturbance observer is proposed to estimate and thereby reject the flexible appendage vibration. Based on the H∞ and Linear Matrix Inequality (LMI) approach, a controller for spacecraft with flexible appendages is proposed to ensure robustness as well as attitude stability with high precision. Stability analysis of the overall closed-loop system is provided via the Lyapunov method. The simulation results of three-axis flexible spacecraft demonstrate the robustness and effectiveness of the proposed method.

Distributed H∞ fusion filtering for multi-sensor networked systems with DoS attacks and sensor saturations

The design problem of a distributed H∞ fusion filter is investigated for multi-sensor networked systems subject to denial of service (DoS) attacks and sensor saturations. The prediction compensation strategy is adopted to solve the problem of packet losses caused by DoS attacks. The local H∞ filter based on single-sensor measurements is obtained via a linear matrix inequality (LMI) method such that the local filtering error system is exponentially stable in the mean square sense and possesses a specified H∞ performance. According to the different H∞ performance levels of local filters, a distributed scalar-weighted fusion filter is constructed. The proposed distributed fusion filter is low complex in computation and has better H∞ performance than the average of all local filters. Simulation studies verify the effectiveness of the proposed algorithms.

Stability analysis and design of cooperative control for linear delta operator system

&lt;abstract&gt;&lt;p&gt;This paper investigates the cooperative state feedback control problem for delta operator-based large-scale systems with independent subsystems. First, the state feedback controller is introduced to interconnect the adjacent subsystems into a closed-loop system. Second, the Lyapunov function in delta domain is constructed, and the linear matrix inequality method is used to design the cooperative state feedback stability controller for the whole large-scale interconnected system. Third, a performance index is introduced for the design of the optimal cooperative state feedback controller. Finally, stability of the closed-loop system is proved on the basis of stability theory, and simulation examples are given for showing the effectiveness of the design method.&lt;/p&gt;&lt;/abstract&gt;