H_∞ Control Based on LMIs for a Class of Time-delay Switched Systems

H 稳定性分析和有在任意的切换的法律下面的推迟的状态的交换系统的控制合成的问题被考虑。借助于 Lyapunov 功能和线性矩阵不平等工具， H 稳定性的足够的状况以线性矩阵不平等被介绍。而且，经由州的反馈的柔韧的 H 控制合成和产量反馈被学习。最后，一个数字例子被给表明建议方法的有效性。

Observer-based adaptive control of uncertain time-delay switched systems with stuck actuator faults

This paper concerns the observer-based adaptive control problem of uncertain time-delay switched systems with stuck actuator faults.Under the case where the original controller cannot stabilize the faulty system,multiple adaptive controllers are designed and a suitable switching logic is incorporated to ensure the closed-loop system stability and state tracking.New delay-independent sufficient conditions for asymptotic stability are obtained in terms of linear matrix inequalities based on piecewise Lyapunov stability theory.On the other hand,adaptive laws for on-line updating of some of the controller parameters are also designed to compensate the effect of stuck failures.Finally,simulation results for reference [1] model show that the design is feasible and efficient.

Finite-Time H∞ Control of Switched Nonlinear Systems under State-Dependent Switching

This paper investigates the finite-time H∞ control problem of switched nonlinear systems via state-dependent switching and state feedback control. Unlike the existing approach based on time-dependent switching strategy, in which the switching instants must be given in advance, the state-dependent switching strategy is used to design switching signals. Based on multiple Lyapunov-like functions method, several criteria for switched nonlinear systems to be finite-time H∞ control are derived. Finally, a numerical example with simulation results is provided to show the validity of the conclusions.

Error reachable set based stabilization of switched linear systems with bounded peak disturbances

This paper investigates the error reachable set based stabilization problem for a class of discrete-time switched linear systems with bounded peak disturbances under persistent dwell-time(PDT)constraint.A double-clockdependent control scheme is presented that can split the disturbed switched system into a nominal system and an error system,and assign to each system a controller scheduled by a clock.A necessary and sufficient convex stability criterion is presented for the nominal system,and is further extended to the stabilization controller design with a nominal clock.In the presence of bounded peak disturbances,another stabilization controller with an error clock is developed for the error system,with the purpose of‘‘minimizing’’the reachable set of the error system by the ellipsoidal techniques.It is demonstrated that the disturbed system is also globally exponentially stable in the sense of converging to an over approximation of the reachable set of the error system,i.e.,a union of a family of bounding ellipsoids,that can also be regarded as the cross section of a tube containing the trajectories of the disturbed system.Two numerical examples are provided to verify the effectiveness of the developed results.

The Time-Scaling Transformation Technique for Optimal Control Problems with Time-Varying Time-Delay Switched Systems

In this paper,we consider a class of optimal control problems where the dynamical systems are time-delay switched systems with the delay being a function of time.By applying the control parameterization method,the control heights and switching times become decision variables that need to be optimized.It is well-known that,for this type problem,the variable switching times cannot be optimized directly.To work around this problem,we introduce a time-scaling transformation technique so that the original system is transformed an equivalent system,which is defined on a new time horizon with fixed switching times.Based on the relationship between the original time scale and the new time scale,we derive the gradients of the objective and constraint functions with respect to the control heights and durations.Then,the new problem can be solved by gradient-based optimization approach.To demonstrate the effectiveness of the time-scaling transformation technique,two example problems are solved.

Group Hybrid Coordination Control of Multi-Agent Systems With Time-Delays and Additive Noises

A new kind of group coordination control problemgroup hybrid coordination control is investigated in this paper.The group hybrid coordination control means that in a whole multi-agent system(MAS)that consists of two subgroups with communications between them,agents in the two subgroups achieve consensus and containment,respectively.For MASs with both time-delays and additive noises,two group control protocols are proposed to solve this problem for the containment-oriented case and consensus-oriented case,respectively.By developing a new analysis idea,some sufficient conditions and necessary conditions related to the communication intensity betw een the two subgroups are obtained for the following two types of group hybrid coordination behavior:1)Agents in one subgroup and in another subgroup achieve weak consensus and containment,respectively;2)Agents in one subgroup and in another subgroup achieve strong consensus and containment,respectively.It is revealed that the decay of the communication impact betw een the two subgroups is necessary for the consensus-oriented case.Finally,the validity of the group control results is verified by several simulation examples.

Lyapunov-Based Output Containment Control of Heterogeneous Multi-Agent Systems With Markovian Switching Topologies and Distributed Delays

This paper considers the mean square output containment control problem for heterogeneous multi-agent systems(MASs)with randomly switching topologies and nonuniform distributed delays.By modeling the switching topologies as a continuous-time Markov process and taking the distributed delays into consideration,a novel distributed containment observer is proposed to estimate the convex hull spanned by the leaders'states.A novel distributed output feedback containment controller is then designed without using the prior knowledge of distributed delays.By constructing a novel switching Lyapunov functional,the output containment control problem is then solved in the sense of mean square under an easily-verifiable sufficient condition.Finally,two numerical examples are given to show the effectiveness of the proposed controller.

Quadratic Stabilization of Switched Uncertain Linear Systems: A Convex Combination Approach

We consider quadratic stabilization for a class of switched systems which are composed of a finite set of continuoustime linear subsystems with norm bounded uncertainties. Under the assumption that there is no single quadratically stable subsystem, if a convex combination of subsystems is quadratically stable, then we propose a state-dependent switching law, based on the convex combination of subsystems, such that the entire switched linear system is quadratically stable. When the state information is not available, we extend the discussion to designing an outputdependent switching law by constructing a robust Luenberger observer for each subsystem.

Robust Controller Design of a Class of Uncertain Switched Fuzzy Systems with Delays

The robust control problem for a class of uncertain switched fuzzy systems with delays is investigated. Firstly,the model of the switched fuzzy system is presented and the parallel distributed compensation( PDC) technology is employed to design fuzzy controllers. Then, based on the convex combination method, a sufficient condition for robust stabilization in terms of linear matrix inequalities( LMIs) is obtained and a switching law is presented.Meanwhile,the Lyapunov-Krasovskii functional is taken to deal with time varying delays. Moreover,an algorithm is applied to finding a solution for a group of convex combination coefficient. Finally,a numerical example is given to demonstrate the effectiveness of the proposed method.

Hybrid-triggered consensus for multi-agent systems with time-delays,uncertain switching topologies, and stochastic cyber-attacks

We propose a new approach to discuss the consensus problem of multi-agent systems with time-varying delayed control inputs, switching topologies, and stochastic cyber-attacks under hybrid-triggered mechanism.A Bernoulli variable is used to describe the hybrid-triggered scheme, which is introduced to alleviate the burden of the network.The mathematical model of the closed-loop control system is established by taking the influences of time-varying delayed control inputs,switching topologies, and stochastic cyber-attacks into account under the hybrid-triggered scheme.A theorem as the main result is given to make the system consistent based on the theory of Lyapunov stability and linear matrix inequality.Markov jumps with uncertain rates of transitions are applied to describe the switch of topologies.Finally, a simulation example demonstrates the feasibility of the theory in this paper.

H∞ Tracking Control for Switched LPV Systems With an Application to Aero-Engines

This paper focuses on the H_∞ model reference tracking control for a switched linear parameter-varying(LPV)model representing an aero-engine. The switched LPV aeroengine model is built based on a family of linearized models.Multiple parameter-dependent Lyapunov functions technique is used to design a tracking control law for the desirable H_∞ tracking performance. A control synthesis condition is formulated in terms of the solvability of a matrix optimization problem.Simulation result on the aero-engine model shows the feasibility and validity of the switching tracking control scheme.

Distributed H2/H∞ Filter Design for Discrete-Time Switched Systems

This paper addresses an infinite horizon distributed H2/H∞ filtering for discrete-time systems under conditions of bounded power and white stochastic signals. The filter algorithm is designed by computing a pair of gains namely the estimator and the coupling. Herein, we implement a filter to estimate unknown parameters such that the closed-loop multi-sensor accomplishes the desired performances of the proposed H2 and H∞ schemes over a finite horizon. A switched strategy is implemented to switch between the states once the operation conditions have changed due to disturbances. It is shown that the stability of the overall filtering-error system with H2/H∞ performance can be established if a piecewise-quadratic Lyapunov function is properly constructed. A simulation example is given to show the effectiveness of the proposed approach.

Minimum Dwell Time for Global Exponential Stability of a Class of Switched Positive Nonlinear Systems

This paper will investigate global exponential stability analysis for a class of switched positive nonlinear systems under minimum dwell time switching, whose nonlinear functions for each subsystem are constrained in a sector field by two odd symmetric piecewise linear functions and whose system matrices for each subsystem are Metzler. A class of multiple time-varying Lyapunov functions is constructed to obtain the computable sufficient conditions on the stability of such switched nonlinear systems within the framework of minimum dwell time switching.All present conditions can be solved by linear/nonlinear programming techniques. An example is provided to demonstrate the effectiveness of the proposed result.

Stability and Robust Stability of Switched Positive Linear Systems With All Modes Unstable

This paper is concerned with the stability and robust stability of switched positive linear systems(SPLSs) whose subsystems are all unstable. By means of the mode-dependent dwell time approach and a class of discretized co-positive Lyapunov functions, some stability conditions of switched positive linear systems with all modes unstable are derived in both the continuous-time and the discrete-time cases, respectively. The copositive Lyapunov functions constructed in this paper are timevarying during the dwell time and time-invariant afterwards. In addition, the above approach is extended to the switched interval positive systems. A numerical example is proposed to illustrate our approach.

Adaptive Consensus of Non-Strict Feedback Switched Multi-Agent Systems With Input Saturations

This paper considers the leader-following consensus for a class of nonlinear switched multi-agent systems(MASs)with non-strict feedback forms and input saturations under unknown switching mechanisms.First,in virtue of Gaussian error functions,the saturation nonlinearities are represented by asymmetric saturation models.Second,neural networks are utilized to approximate some unknown packaged functions,and the structural property of Gaussian basis functions is introduced to handle the non-strict feedback terms.Third,by using the backstepping process,a common Lyapunov function is constructed for all the subsystems of the followers.At last,we propose an adaptive consensus protocol,under which the tracking error under arbitrary switching converges to a small neighborhood of the origin.The effectiveness of the proposed protocol is illustrated by a simulation example.

Global Practical Stabilization of Discrete-Time Switched Affine Systems via a General Quadratic Lyapunov Function and a Decentralized Ellipsoid

This paper addresses the problem of global practical stabilization of discrete-time switched affine systems via statedependent switching rules.Several attempts have been made to solve this problem via different types of a common quadratic Lyapunov function and an ellipsoid.These classical results require either the quadratic Lyapunov function or the employed ellipsoid to be of the centralized type.In some cases,the ellipsoids are defined dependently as the level sets of a decentralized Lyapunov function.In this paper,we extend the existing results by the simultaneous use of a general decentralized Lyapunov function and a decentralized ellipsoid parameterized independently.The proposed conditions provide less conservative results than existing works in the sense of the ultimate invariant set of attraction size.Two different approaches are proposed to extract the ultimate invariant set of attraction with a minimum size,i.e.,a purely numerical method and a numerical-analytical one.In the former,both invariant and attractiveness conditions are imposed to extract the final set of matrix inequalities.The latter is established on a principle that the attractiveness of a set implies its invariance.Thus,the stability conditions are derived based on only the attractiveness property as a set of matrix inequalities with a smaller dimension.Illustrative examples are presented to prove the satisfactory operation of the proposed stabilization methods.

Output Feedback Based Admissible Control of Switched Linear Singular Systems

The admissibility analysis and robust admissible control problem of the uncertain discrete-time switched linear singular (SLS) systems for arbitrary switching laws are investigated. Based on linear matrix inequalities, some sufficient conditions are given for: A) the existence of generalized common Lyapunov solution and the admissibility of the SLS systems for arbitrary switching laws, B) the existence of static output feedback control laws ensuring the admissibility of the closed-loop SLS systems for arbitrary switching laws and norm-bounded uncertainties.

Iterative Learning Control for a Class of Linear Discrete-time Switched Systems

在这份报纸，反复的学习控制(ILC ) 与任意的切换的信号为线性分离时间的交换系统的一个类被考虑。交换系统重复地在有限时间间隔期间被操作，这被假定，然后第一个顺序 P 类型 ILC 计划能被用来完成完美的追踪在上自始至终间隔。由超级向量途径，为在重复领域的如此的 ILC 系统的一个集中条件能被给。理论分析被模拟支持。

Admissibility analysis and control synthesis for switched linear singular systems

The problem of admissibility analysis and control synthesis of discrete-time switched linear singular (SLS) systems for arbitrary switching laws is solved.By using the switched Lyapunov function approach,some new sufficient conditions under which the SLS system is admissible for arbitrary switching laws are derived in terms of linear matrix inequalities(LMIs).Based on the admissibility results,control synthesis is then to design switched state feedback and static output feedback controllers,guaranteeing that the resulting closed-loop system is admissible.The presented results can be viewed as the extensions of previous works on switched Lyapunov function approach from the regular switched systems to singular switched cases.Examples are provided to demonstrate the reduced conservatism and effectiveness of the proposed conditions.