Regional eigenvalue-clustering robustness of linear uncertain multivariable output feedback PID control systems

This paper proposes a time domain approach to deal with the regional eigenvalue-clustering robustness analysis problem of linear uncertain multivariable output feedback proportional-integral-derivative (PID) control systems. The robust regional eigenvalue-clustering analysis problem of linear uncertain multivariable output feedback PID control systems is converted to the regional eigenvalue-clustering robustness analysis problem of linear uncertain singular systems with static output feedback controller. Based on some essential properties of matrix measures, a new sufficient condition is proposed for ensuring that the closed-loop singular system with both structured and mixed quadratically-coupled parameter uncertainties is regular and impulse-free, and has all its finite eigenvalues retained inside the same specified region as the nominal closed-loop singular system does. Two numerical examples are given to illustrate the application of the presented sufficient condition.     

Delay-dependent non-fragile robust stabilization and H∞ control of uncertain stochastic systems with time-varying delay and nonlinearity

This paper deals with the problems of non-fragile robust stochastic stabilization and robust H_∞ control for uncertain stochastic nonlinear time-delay systems. The parameter uncertainties are assumed to be time-varying norm-bounded appearing in both state and input matrices. The time-delay is unknown and time-varying with known bounds. The non-fragile robust stochastic stabilization problem is to design a memoryless non-fragile state feedback controller such that the closed-loop system is robustly stochastically stable for all admissible parameter uncertainties. The purpose of robust H_∞ control problem, in addition to robust stochastical stability requirement, is to reduce the effect of the disturbance input on the controlled output to a prescribed level. Using the Lyapunov functional method and free-weighting matrices, delay-dependent sufficient conditions for the solvability of these problems are established in terms of linear matrix inequality (LMI). Numerical example is provided to show the effectiveness of the proposed theoretical results.     

Design of adaptive sliding mode controller for robust tracking and model following

The problem of the robust tracking and model following for a class of linear systems with time-varying parameter uncertainties, multiple delayed state perturbations and external disturbance is investigated in this paper. The algorithm is based on the adaptive sliding mode control. The proposed method does not need a priori knowledge of upper bounds on the norm of the uncertainties, but estimates them by using the adaptation technique so that the reaching condition can be satisfied. This scheme guarantees the closed-loop system stability and zero-tracking error in the presence of time-varying parameter uncertainties, multiple delayed state perturbations and external disturbance. Finally, simulation results demonstrate the efficacy of the proposed control methodology.     

Robust finite-time stability of discrete time systems with interval time-varying delay and nonlinear perturbations

The problem of finite-time stability (FTS) for discrete-time systems with interval time-varying delay, nonlinear perturbations and parameter uncertainties is considered in this paper. In order to obtain less conservative stability criteria, a finite sum inequality with delayed states is proposed. Some sufficient conditions of FTS are derived in the form of the linear matrix inequalities (LMIs) by using Lyapunov–Krasovskii-like functional (LKLF) with power function and single/double summation terms. More precisely estimations of the upper bound of the initial value of LKLF and the lower bound of LKLF are proposed. As special cases, the FTS of nominal discrete-time systems with constant or time-varying delay is considered. The numerical examples are presented to illustrate the effectiveness of the results and their improvement over the existing literature.     

Robust formation control for uncertain multi-agent systems

Robust formation problems for linear multi-agent systems with uncertainties and external disturbances are investigated in this paper. The model of each agent can be described by a nominal linear system combined with external disturbances and uncertainties which include parameter perturbations and nonlinear uncertainties. A more general bound of uncertainties is introduced. A robust formation controller, which consists of a nominal controller and a robust compensator, is proposed to achieve the desired state formation and restrain the influence of uncertainties and disturbances. Furthermore, sufficient conditions for time-varying formation feasibility are introduced and proved. Finally, a numerical example is provided to demonstrate the theoretical results.     

Stability analysis of a class of variable fractional-order uncertain neutral-type systems with time-varying delay

Variable fractional-order (VFO) differential equations are a beneficial tool for describing the nonlinear behavior of complex dynamical phenomena. In comparison with the constant FO derivatives, it describes the memory properties of such systems that can vary in the time domain and spatial location. This article investigates the stability and stabilization of VFO neutral systems in the presence of time-varying structured uncertainties and time-varying delay. FO Lyapunov theorem is adopted to achieve order-dependent and delay-dependent criteria for both nominal and uncertain VFO neutral delay systems. The obtained conditions are given in respect of linear matrix inequality by designing a delayed state feedback controller. Simulations verify the main results.     

Finite-time guaranteed cost control for uncertain delayed switched nonlinear stochastic systems

This paper studies the finite-time guaranteed cost control problem for switched nonlinear stochastic systems with parameter uncertainties and time-varying delays. By choosing a model-dependent and delay-dependent Lyapunov-Krasovskii functional, applying the average dwell time approach and the Gronwall inequality, some novel sufficient conditions are derived to ensure that the switched nonlinear stochastic closed-loop system is finite-time stochastically stable and an upper bound is given on the performance index. The obtained nonlinear matrix is transformed into a linear matrix form, and then the feedback controller gains of the switched nonlinear stochastic systems with time-varying delay are obtained. Finally, two simulation examples are designed to verify the effectiveness of the suggested approach.     

Design of observers for a class of discrete-time uncertain nonlinear systems with time delay

This paper is concerned with the problem of observer design for a class of discrete-time Lipschitz nonlinear state delayed systems with, or without parameter uncertainty. The nonlinearities are assumed to appear in both the state and measured output equations. For both the cases with and without norm-bounded time-varying parameter uncertainties, a design method is proposed, which involves solving a linear matrix inequality (LMI). When a certain LMI is satisfied, the explicit expression of a desired nonlinear observer is also presented. An example is provided to demonstrate the applicability of the proposed approach.     

On hyper-exponential stability and stabilization of linear systems by bounded linear time-varying controllers

Hyper-exponential stability analysis and hyper-exponential stabilization of linear systems by bounded linear time-varying feedback are investigated in this paper. On the one hand, we propose some Lyapunov-like hyper-exponential stability theorems (both global and local) based on the comparison principle and the concepts of hyper-exponentially stable functions and hyper-exponentially increasing functions. On the other hand, we establish methods to design bounded linear time-varying controllers such that hyper-exponential stability of linear time-invariant systems can be guaranteed. The key design tool is the utilization of a time-varying parameter contained in the controller and the properties of solution to a parametric Lyapunov equation. Both state feedback and observer-based output feedback are accommodated. As a further result, hyper-exponential semi-global stabilization for linear systems by bounded controls is discussed. Finally, the validity of the proposed schemes is illustrated through numerical simulations on spacecraft rendezvous control system.     

Advanced controller synthesis for fuzzy parameter varying systems

A novel nonlinear time-varying model termed as the fuzzy parameter varying (FPV) system is proposed in this research, which inherits both advantages of the conventional T-S fuzzy system in dealing with nonlinear plants and strengths of the linear parameter varying (LPV) system in handling time-varying features. It is, therefore, an attractive mathematical model to efficiently approximate a nonlinear time-varying plant or to serve as a type of time-varying controller. Using the full block S-procedure, sufficient stability conditions have been derived in the form of linear matrix inequalities (LMIs) to test quadratic stability of the open-loop FPV system. Moreover, sufficient conditions have been derived on synthesizing both state feedback and dynamical output feedback fuzzy gain-scheduling controllers that can stabilize the FPV system. An inverted pendulum with a variable length pole is utilized to demonstrate advantages of the FPV system compared to the conventional T-S fuzzy system in representing a practical time-varying nonlinear plant and to validate the controller synthesis conditions.     

Robust stability of uncertain second-order linear time-varying systems

This paper is concerned with robust stability analysis of second-order linear time-varying (SLTV) systems with time-varying uncertainties (perturbations). With the specific Lyapunov functions, a simple and neat algebraic criterion for testing uniformly asymptotic stability of SLTV systems are derived. Without transformation to a system of first-order equations, the new conditions are imposed directly on the time-varying coefficient matrices of the system. The main feature of the proposed algebraic criterion is that the uncertain coefficient matrices are time-varying and not necessarily symmetric. Finally, the proposed stability conditions are used to design the extending space structures system of the spacecraft. Simulation results are provided to illustrate the convenience and effectiveness of the proposed method.     

Dissipative output feedback control for semi-Markovian jump systems under hybrid cyber-attacks

In this paper, the dissipativity-based dynamic output feedback controller (DOFC) design for Semi-Markovian jump systems under stochastic cyber-attacks is first proposed. It is assumed that the time-varying uncertainties obey Bernoulli-distribution and transition probability matrix is time-varying and partially accessed. By utilizing the dissipativity-based technique, sufficient conditions for the existence of the DOFC are obtained to ensure the exponential stability with a strict dissipative performance of the resulted system. Next, the proposed results are improved by fractionalizing the time-varying transition probability matrix and the corresponding DOFC gains are obtained by cone complementarity linearization algorithm. Simulations results are provided to demonstrate the effectiveness and theoretical value of the proposed dissipativity-based DOFC design method.     

Controller design for 2-D stochastic nonlinear Roesser model: A probability-dependent gain-scheduling approach

This note is concerned with the static output feedback control problem for two-dimensional (2-D) uncertain stochastic nonlinear systems. The systems under consideration are subjected to time delays, multiplicative noises and randomly occurring missing measurements. A random variable sequence following the Bernoulli distribution with time-varying probability is employed to character the missing measurements which are assumed to occur in a random way. A new gain-scheduling method based on the time-varying probability parameter is proposed to accomplish the design task. By constructing a suitable Lyapunov functional, sufficient conditions to guarantee the systems to be mean-square asymptotically stable are established. The addressed 2-D controller design problem can be reduced to a convex optimization problem by some mathematical techniques. In the last section, a numerical example and the comparative analysis are provided to illustrate the efficiency of our proposed design approach.     

Cooperative output regulation problem of multi-agent systems with stochastic packet dropout and time-varying communication delay

In this paper, we deal with the cooperative output regulation problem of linear multi-agent systems on a directed network topology subject to both stochastic packet dropout and time-varying communication delay. On the basis of introducing a queuing mechanism, a distributed state feedback control algorithm is proposed. Then the continuous-time multi-agent systems with piece-wise constant control are converted into discrete-time systems. Under some standard assumptions, the necessary and sufficient conditions under which the tracking errors of followers approach to the origin asymptotically are proposed for different exosystems. Finally, the proposed results are verified via two examples.     

Non-fragile guaranteed cost control for uncertain stochastic nonlinear time-delay systems

This paper deals with the problem of non-fragile guaranteed cost control for a class of uncertain stochastic nonlinear time-delay systems. The parametric uncertainties are assumed to be time-varying and norm bounded. The time-delay factors are unknown and time-varying with known bounds. The aim of this paper is to design a memoryless non-fragile state feedback control law such that the closed-loop system is stochastically asymptotically stable in the mean square for all admissible parameter uncertainties and the closed-loop cost function value is not more than a specified upper bound. A new sufficient condition for the existence of such controllers is presented based on the linear matrix inequality (LMI) approach. Then, a convex optimization problem is formulated to select the optimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function. Numerical example is given to illustrate the effectiveness of the developed techniques.     

Parameter-dependent robust stability for uncertain Markovian jump systems with time delay

In this paper, the problem of parameter-dependent robust stability analysis is addressed for uncertain Markovian jump linear systems (MJLSs) with polytopic parameter uncertainties and time-varying delay. By constructing parameter-dependent Lyapunov functional, some sufficient conditions are developed to enable robust exponential mean square stability for the systems. New parameter-dependent robust stability criteria for MJLSs are established in the form of linear matrix inequalities (LMIs), which can be solved efficiently by the interior-point algorithm. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.     

Adaptive event-triggered H∞ fuzzy filtering for interval type-2 T–S fuzzy-model-based networked control systems with asynchronously and imperfectly matched membership functions

This paper is concerned with the network-based H_∞ fuzzy filtering for non-linear systems with parameter uncertainties under a novel adaptive discrete event-triggered communication scheme (DETCS). Based on interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy model, the non-linear systems with parameter uncertainties are represented as a class of IT2 T–S fuzzy systems. In the design process, a novel adaptive DETCS is proposed to reduce the usage of system resources and adapt the variation of plant output, and a novel networked IT2 T–S fuzzy filter is applied to improve the flexibility of filter design. By employing the time-delay systems modeling method, the filtering-error-system is modeled as a class of interval time-varying delayed IT2 T–S fuzzy systems with asynchronously and imperfectly matched membership functions, and further conditionally expressed as a favorable form. Then, some relaxed stability criteria are established to determine that this class of delayed IT2 T–S fuzzy systems is asymptotically stable with a prescribed H_∞ disturbance attenuation performance. Also, the co-design of parameter matrices of adaptive DETCS and filter is implemented. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method.     

Passivity-based boundary control for delay reaction-diffusion systems

Passivity-based boundary control is considered for time-varying delay reaction-diffusion systems (DRDSs) with boundary input-output. By virtue of Lyapunov functional method and inequality techniques, sufficient conditions are obtained for input strict passivity and output strict passivity of DRDSs, respectively. When the parameter uncertainties appear in DRDSs, sufficient conditions are presented to guarantee the robust passivity. Moreover, we apply our theoretical results to the synchronization problem of coupled delay reaction-diffusion systems and get the criterion to ensure the asymptotic synchronization. Finally, numerical simulations are provided to show the validity of our theoretical results.     

一类不确定时延非线性大系统的分散控制

本文研究了一类具有关联延迟和系统参数不确定的非线性大系统的分散控制问题,系统的匹配/非匹配不确定参数范数有界。首先基于状态观测器设计时延独立的动态输出反馈控制律，并根据 稳定性理论推导并证明了在该控制律作用下系统稳定的充分条件。最后给出一个数值例子来说明本文结果的可行性，仿真结果表明设计出的控制器不仅使得闭环系统稳定而且保证系统不受参数不确定和时延的影响。     

Dissipativity analysis and synthesis of a class of nonlinear systems with time-varying delays

In this paper, new results are established for the delay-independent and delay-dependent problems of dissipative analysis and state-feedback synthesis for a class of nonlinear systems with time-varying delays with polytopic uncertainties. This class consists of linear time-delay systems subject to nonlinear cone-bounded perturbations. Both delay-independent and delay-dependent dissipativity criteria are established as linear matrix inequality-based feasibility tests. The developed results in this paper for the nominal system encompass available results on H_∞ approach, passivity and positive realness for time-delay systems as special cases. All the sufficient stability conditions are cast. Robust dissipativity as well as dissipative state-feedback synthesis results are also derived. Numerical examples are provided to illustrate the theoretical developments.