Distributed solver for linear matrix inequalities: an optimization perspective

In this paper,we develop a distributed solver for a group of strict(non-strict)linear matrix inequalities over a multi-agent network,where each agent only knows one inequality,and all agents co-operate to reach a consensus solution in the intersection of all the feasible regions.The formulation is transformed into a distributed optimization problem by introducing slack variables and consensus constraints.Then,by the primal–dual methods,a distributed algorithm is proposed with the help of projection operators and derivative feedback.Finally,the convergence of the algorithm is analyzed,followed by illustrative simulations.

Event-Triggered Finite-Time H∞ Filtering for Discrete-Time Nonlinear Stochastic Systems

This paper addresses the problem of event-triggered finite-time H∞ filter design for a class of discrete-time nonlinear stochastic systems with exogenous disturbances. The stochastic Lyapunov-Krasoviskii functional method is adopted to design a filter such that the filtering error system is stochastic finite-time stable (SFTS) and preserves a prescribed performance level according to the pre-defined event-triggered criteria. Based on stochastic differential equations theory, some sufficient conditions for the existence of H∞ filter are obtained for the suggested system by employing linear matrix inequality technique. Finally, the desired H∞ filter gain matrices can be expressed in an explicit form.

Self-triggered Consensus Control for Linear Multi-agent Systems With Input Saturation

In this paper, we study the consensus problem for a class of linear multi-agent systems(MASs) with consideration of input saturation under the self-triggered mechanism. In the context of discrete-time systems, a self-triggered strategy is developed to determine the time interval between the adjacent triggers. The triggering condition is designed by using the current sampled consensus error. Furthermore, the consensus control protocol is designed by means of a state feedback approach. It is shown that the considered multi-agent systems can reach consensus with the presented algorithm. Some sufficient conditions are proposed in the form of linear matrix inequalities(LMIs) to show the positively invariant property of the domain of attraction(DOA). Moreover, some sufficient conditions of controller synthesis are provided to enlarge the volume of the DOA and obtain the control gain matrix. A numerical example is simulated to demonstrate the effectiveness of the theoretical analysis results.

Distributed Model Predictive Control with Actuator Saturation for Markovian Jump Linear System

This paper is concerned with the distributed model predictive control(MPC) problem for a class of discrete-time Markovian jump linear systems(MJLSs) subject to actuator saturation and polytopic uncertainty in system matrices. The global system is decomposed into several subsystems which coordinate with each other. A set of distributed controllers is designed by solving a min-max optimization problem in terms of the solutions of linear matrix inequalities(LMIs). An iterative algorithm is developed to achieve the online computation. Finally,a simulation example is employed to show the effectiveness of the proposed algorithm.

Stability Analysis of Cyber-Physical Micro Grid Load Frequency Control System with Time-Varying Delay and Non-Linear Load Perturbations

In a cyber-physical micro-grid system,wherein the control functions are executed through open communication channel,stability is an important issue owing to the factors related to the time-delay encountered in the data transfer.Transfer of feedback variable as discrete data packets in communication network invariably introduces inevitable time-delays in closed loop control systems.This delay,depending upon the network traffic condition,inherits a time-varying characteristic;nevertheless,it adversely impacts the system performance and stability.The load perturbations in a micro-grid system are considerably influenced by the presence of fluctuating power generators like wind and solar power.Since these non-conventional energy sources are integrated into the power grid through power electronic interface circuits that usually works at high switching frequency,noise signals are introduced into the micro-grid system and these signals gets super-imposed to the load variations.Based on this back ground,in this paper,the delay-dependent stability issue of networked micro-grid system combined with time-varying feedback loop delay and uncertain load perturbations is investigated,and a deeper insight has been presented to infer the impact of time-delay on the variations in the system frequency.The classical Lyapunov-Krasovskii method is employed to address the problem,and using a standard benchmark micro-grid system,and the proposed stability criterion is validated.

Stabilizing controller design for nonlinear fractional order systems with time varying delays

To deal with stabilizing of nonlinear affine fractional order systems subject to time varying delays,two methods for finding an appropriate pseudo state feedback controller are discussed.In the first method,using the Mittag-Lefler function,Laplace transform and Gronwall inequality,a linear stabilizing controller is derived,which uses the fractional order of the delayed system and the upper bound of system nonlinear functions.In the second method,at first a sufficient stability condition for the delayed system is given in the form of a simple linear matrix inequality(LMI)which can easily be solved.Then,on the basis of this result,a stabilizing pseudo-state feedback controller is designed in which the controller gain matrix is easily computed by solving an LMI in terms of delay bounds.Simulation results show the effectiveness of the proposed methods.

Robust Stability Criteria for Neutral Systems with Interval Time-Varying Delays and Nonlinear Perturbations

This paper investigates the problem of delay-dependent robust stability analysis for a class of neutral systems with interval time-varying delays and nonlinear perturbations. Such nonlinear perturbations are with time-varying but norm-bounded characteristics. Based on a new Lyapunov-Krasovskii functional together with a free-weighting matrices technique,improved delay-dependent stability criteria are established. It is shown that less conservative results can be obtained in terms of linear matrix inequalities( LMIs). Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed approach.

Synchronization of High-order Discrete-time Linear Complex Networks with Time-varying Delays

Synchronization of high-order discrete-time complex networks with undirected topologies is studied and the impacts of time delays are investigated. Firstly,by the state decomposition,synchronization problems are transformed into asymptotic stability ones of multiple lower dimensional time-delayed subsystems. Then,linear matrix inequality( LMI) criteria for synchronization are given,which can guarantee the scalability of complex networks since they only include three LMI constraints independent of the number of agents. Moreover,an explicit expression of the synchronization function is presented,which can describe the synchronization behavior of all agents in complex networks. Finally,a numerical example is given to demonstrate the theoretical results,where it is shown that if the gain matrices of synchronization protocols satisfy LMI criteria for synchronization,synchronization can be achieved.

Robust non-fragile control for discrete-delay nonlinear large-scale systems

Time-delays,due to the information transmission between subsystems,naturally exist in large-scale systems and the existence of the delay is frequently a source of instability. This paper considers the problems of robust non-fragile fuzzy control for a class of uncertain discrete nonlinear large-scale systems with time-delay and controller gain perturbations described by T-S fuzzy model. An equivalent T-S fuzzy model is represented for discrete-delay nonlinear large-scale systems. A sufficient condition for the existence of such non-fragile controllers is further derived via the Lyapunov function and the linear matrix inequality( LMI) approach. Simulation results demonstrate the feasibility and the effectiveness of the proposed design and the proper stabilization of the system in spite of controller gain variations and uncertainties.

Exponential Stability for a Class of Uncertain Linear Systems with a Single Time-Delay (or Multiple Time-Delays)

This paper investigates the issue of exponential stability for a class of uncertain linear systems with a single time-delay (or multiple time-delays). We consider that the uncertainties are the parameter disturbance and the external disturbance, both of which are stochastic. The external disturbances involve not only the current state x(t) but also the delayed state x(t - τ). By means of the Lyapunov-Krasovskii functional, the sufficient conditions on exponential stability for the uncertain linear systems with a single time-delay (or multiple time-delays) are performed in the form of the linear matrix inequality (LMI). Selecting the suitable matrices P (or ) and Q (or ) and parameter β (or ), we can also get the bounds of the state variables for the single time-delay (or multiple time-delays) systems. In order to stabilize the solution of the single time-delay (or multiple time-delays) systems at the equilibrium point, we designed the state feedback control. Thus, the corresponding stabilization criteria are given. Finally, Numerical simulations show that a small disturbance can make a great change to the state variables of the systems. When the feedback gain control is added, the state variables of the systems can quickly stabilize at the equilibrium point. This also shows the effectiveness of the proposed method.

Data-Driven Control of Linear Systems via Quantized Feedback

Quantized feedback control is fundamental to system synthesis with limited communication capacity.In sharp contrast to the existing literature on quantized control which requires an explicit dynamical model,the authors study the quadratic stabilization and performance control problems with logarithmically quantized feedback in a direct data-driven framework,where the system state matrix is not exactly known and instead,belongs to an ambiguity set that is directly constructed from a finite number of noisy system data.To this end,the authors firstly establish sufficient and necessary conditions via linear matrix inequalities for the existence of a common quantized controller that achieves our control objectives over the ambiguity set.Then,the authors provide necessary conditions on the data for the solvability of the LMIs,and determine the coarsest quantization density via semi-definite programming.The theoretical results are validated through numerical examples.

H∞ Control for Externally Excited Building Structures with Active Mass Damper under Actuator Saturation

This paper investigates the application of active mass dampers to mitigate the vibrations of building structures subjected to unknown external excitations under controller saturation conditions. By utilizing an H∞ control strategy, the optimal state feedback controller is derived by solving the linear matrix inequality problem for controller saturation. Case studies show that the proposed controller is capable of stabilizing the closed-loop system with good control performance and effectively suppressing vibrations in building structures under unknown external excitation. When compared to controllers that do not consider saturation, the proposed controller requires lower gain and results in reduced energy consumption. The research findings provide valuable insights for addressing real-world building structure control problems, contributing to both theoretical significance and practical applications.

LMI Consensus Condition for Discrete-time Multi-agent Systems

This paper examines a consensus problem in multiagent discrete-time systems, where each agent can exchange information only from its neighbor agents. A decentralized protocol is designed for each agent to steer all agents to the same vector. The design condition is expressed in the form of a linear matrix inequality. Finally, a simulation example is presented and a comparison is made to demonstrate the effectiveness of the developed methodology.

New Robust Exponential Stability Analysis for Uncertain Neural Networks with Time-varying Delay

In this paper, the global robust exponential stability is considered for a class of neural networks with parametric uncer-tainties and time-varying delay. By using Lyapunov functional method, and by resorting to the new technique for estimating the upper bound of the derivative of the Lyapunov functional, some less conservative exponential stability criteria are derived in terms of linear matrix inequalities (LMIs). Numerical examples are presented to show the effectiveness of the proposed method.

Polyhedral Feasible Set Computation of MPC-Based Optimal Control Problems

Feasible sets play an important role in model predictive control(MPC) optimal control problems(OCPs). This paper proposes a multi-parametric programming-based algorithm to compute the feasible set for OCP derived from MPC-based algorithms involving both spectrahedron(represented by linear matrix inequalities) and polyhedral(represented by a set of inequalities) constraints. According to the geometrical meaning of the inner product of vectors, the maximum length of the projection vector from the feasible set to a unit spherical coordinates vector is computed and the optimal solution has been proved to be one of the vertices of the feasible set. After computing the vertices,the convex hull of these vertices is determined which equals the feasible set. The simulation results show that the proposed method is especially efficient for low dimensional feasible set computation and avoids the non-unicity problem of optimizers as well as the memory consumption problem that encountered by projection algorithms.

PASSIVE CONTROL FOR A CLASS OF UNCERTAIN TIME-DELAY SYSTEMS

This paper focuses on the passive control for a class of linear time delay system with norm bounded time varying parameter uncertainties by using a linear matrix inequality (LMI) approach. A sufficient condition under which the uncertain time delay system is quadratically stable and strictly passive for all admissible uncertainties was derived. It is shown that the solvability of problem of the robust passive controller design is implied by the feasibility of a linear matrix inequality.

ROBUST DISSIPATIVE CONTROL FOR STATE-DELAYED SYSTEMS WITH DISSIPATIVE UNCERTAINTY

This paper focused on a class of linear state-delayed systems with or without uncertainty. As for uncertain systems, dissipative uncertainty description contains norm-bounded and positive real uncertainties as special cases. The paper is concerned with the design of dissipative static state feedback controllers such that the closed-loop system is (robustly) asymptotically stable and strictly (Q,S,R)-dissipative. Sufficient conditions for the existence of the quadratic dissipative state feedback controllers are obtained by using a linear matrix inequality (LMI) approach. It is shown that the solvability of dissipative controller design problem is implied by the feasibility of LMIs. The main results of this paper unify the existing results on H ∞ control and passive control.

LMI-BASED AERO-ENGINE CONTROLLER DESIGN

The problem of analysis and synthesis of robust control is addressed in this work. The approach transferring the robust control design into Linear Matrix Inequality(LMI) is provided. The LMI standard structure of robust controller is also given and the controller is obtained through solving three LMIs. As an example, a robust control law is designed to the twin spool turbojet engine system using the given approach. The result shows that LMI approach is feasible.

Event-Triggered Finite-Time <i>H</i>_∞Control for Switched Stochastic Systems

This paper investigates the problem of event-triggered finite-time H∞ control for a class of switched stochastic systems. The main objective of this study is to design an event-triggered state feedback H∞ controller such that the resulting closed-loop system is finite-time bounded and satisfies a prescribed H∞ level in some given finite-time interval. Based on stochastic differential equations theory and average dwell time approach, sufficient conditions are derived to ensure the finite-time stochastic stability with the prescribed H∞ performance for the relevant closed-loop system by employing the linear matrix inequality technique. Finally, the desired state feedback H∞ controller gain matrices can be expressed in an explicit form.

Robust Finite-Time H∞ Filtering for ItôStochastic Systems

This paper investigates the problem of robust finite-time H∞ filter design for Itô stochastic systems. Based on linear matrix inequalities (LMIS) techniques and stability theory of stochastic differential equations, stochastic Lyapunov function method is adopted to design a finite-time H∞ filter such that, for all admissible uncertainties, the filtering error system is stochastic finite-time stable (SFTS). A sufficient condition for the existence of a finite-time H∞ filter for the stochastic system under consideration is achieved in terms of LMIS. Moreover, the explicit expression of the desired filter parameters is given. A numerical example is provided to illustrate the effectiveness of the proposed method.