离散时间两层切换系统的鲁棒指数几乎处处稳定性

提出了一种新类型的切换系统——两层切换系统(Two-level switched systems, TSSs),其顶层切换是确定的,底层切换为随机的且由多个Markov链支配.基于持续驻留时间(Persistent dwell-time, PDT)方法,研究了TSS存在参数不确定性情况下的鲁棒指数几乎处处(Exponential almost sure, EAS)稳定性,以线性矩阵不等式(Linear matrix inequality, LMI)形式给出了一个充分条件.最后通过数值仿真例子验证了本文方法的有效性.     

Dynamic output feedback control of saturated switched delay systems under the PDT switching

This paper is devoted to saturated control of switched delay systems. The main focus is to find a suitable switching law and saturated output feedback controllers such that the closed‐loop systems are asymptotically stable and have the disturbance tolerance/rejection capacity. A mixed slow/arbitrary switching approach, so‐called persistent dwell time (PDT) switching, is used to design the switching law. Compared with the slow switching, it is more general and leads to more flexibility in the process of constructing switching signals. More importantly, the proposed PDT is dependent on state delay, which includes the previous delay‐independent PDT. Next, time‐varying ellipsoids and a prescribe l₂‐gain are introduced to characterize the disturbance tolerance and rejection capacities of systems, respectively. Based on the proposed results, the relation between delay‐dependent PDT and level of disturbance tolerance/rejection is shown. Finally, saturated controllers working in time‐varying hull controllable regions are designed. Thus, the considered problem is solved. An example is exploited to illustrate the effectiveness of the proposed results. Copyright © 2016 John Wiley & Sons, Ltd.     

离散双切换线性正系统的L1增益性能分析

离散时间双切换线性正系统是同时受到确定切换信号和Markov随机切换信号共同影响的系统。鲁棒稳定以及扰动抑制问题是研究混杂系统稳定性的重要问题,但双切换正系统的扰动抑制问题研究较少。基于此研究背景,提出了新型的切换系统——具有指数不确定性的离散时间双切换线性正系统(DDSLPS),通过构建Co-positive Lyapunov能量衰减函数,利用线性编程(LP)得到确保DDSLPS在持续驻留时间(PDT)约束下系统满足鲁棒指数几乎处处稳定(Robust-EAS)的充分条件。另外,将此方法推广到DDSLPS的L1增益分析中,得到闭环系统在鲁棒指数几乎处处稳定下满足L1性能指标x的充分条件。利用Matlab数值仿真,验证了所用方法的有效性和所得结果的正确性。     

Exponential stability and robust H∞ control of a class of discrete-time switched non-linear systems with time-varying delays via T-S fuzzy model

This paper deals with stability and robust H_∞ control of discrete-time switched non-linear systems with time-varying delays. The T-S fuzzy models are utilised to represent each sub-non-linear system. Thus, with two level functions, namely, crisp switching functions and local fuzzy weighting functions, we introduce a discrete-time switched fuzzy systems, which inherently contain the features of the switched hybrid systems and T-S fuzzy systems. Piecewise fuzzy weighting-dependent Lyapunov–Krasovskii functionals (PFLKFs) and average dwell-time approach are utilised in this paper for the exponentially stability analysis and controller design, and with free fuzzy weighting matrix scheme, switching control laws are obtained such that H_∞ performance is satisfied. The conditions of stability and the control laws are given in the form of linear matrix inequalities (LMIs) that are numerically feasible. The state decay estimate is explicitly given. A numerical example and the control of delayed single link robot arm with uncertain part are given to demonstrate the efficiency of the proposed method.     

H∞ Adaptive tracking control for switched systems based on an average dwell-time method

This paper investigates the H_∞ state tracking model reference adaptive control (MRAC) problem for a class of switched systems using an average dwell-time method. First, a stability criterion is established for a switched reference model. Then, an adaptive controller is designed and the state tracking control problem is converted into the stability analysis. The global practical stability of the error switched system can be guaranteed under a class of switching signals characterised by an average dwell time. Consequently, sufficient conditions for the solvability of the H_∞ state tracking MRAC problem are derived. An example of highly manoeuvrable aircraft technology vehicle is given to demonstrate the feasibility and effectiveness of the proposed design method.     

时变时滞连续切换奇异系统的一致有限时间稳定分析

讨论一类含有时变时滞的连续时间切换奇异系统的一致有限时间稳定、有限时间有界和状态反馈镇定问题. 在给定任意的切换规则下, 运用多Lyapunov 函数和平均驻留时间方法设计使得闭环系统一致有限时间稳定和有限时间有界的状态反馈控制器, 同时给出基于线性矩阵不等式表示的控制器存在的充分条件. 最后通过数值算例表明了所提出方法的合理性和有效性.

     

Dual approach to stability and stabilisation of uncertain switched positive systems

This paper addresses two kinds of dual approaches to stability and stabilisation of uncertain switched positive systems under arbitrary switching and average dwell-time switching, respectively. The uncertainties in systems refer to polytopic ones. A new parameter-dependent switched linear copositive Lyapunov function is first proposed for uncertain switched positive systems. By using the new Lyapunov function associated with arbitrary switching and average dwell-time switching, respectively, sufficient conditions for the stability of the systems are established. Two alternative stability criteria based on two kinds of dual approaches are addressed. It is shown that the alternative criteria hold for not only the primal switched positive system but also its dual system. Then, the stabilisation of primal and dual switched positive systems under arbitrary switching and average dwell-time switching is solved, respectively. All present conditions are solvable in terms of linear programming. By some comparisons with existing results, the less conservativeness of the obtained results is verified. Finally, a practical example is provided to illustrate the effectiveness of the theoretical findings.     

Supervisory control with state-dependent dwell-time logic and constraints

The paper deals with the supervisory control of a nonlinear uncertain system in which the switching is directed by the recently introduced state-dependent dwell-time switching logic. The proposed supervisory control architecture is shown to regulate to zero the state of the system without requiring the switching to stop in finite time. A significant class of systems to which the control architecture can be applied is the class of linear systems with input saturation.     

Persistent Dwell-Time Switched Nonlinear Systems: Variation Paradigm and Gauge Design

Asymptotic gain and adaptive control are studied for persistent dwell-time switched systems. Ultimate variations of auxiliary functions are considered for existence of asymptotic gain and a gauge design is introduced for switching-uniform adaptive control by partial state feedback and output feedback of switched systems subject to unmeasured dynamics and persistent dwell-time switching. The usage of the controlled dynamics as a gauge for the instability mode of the unmeasured dynamics makes it possible to design a control rendering the evolution of the overall system interchangeably driven by the stable modes of the controlled and unmeasured dynamics. Unmeasured-state dependent control gains are dealt with and unknown time-varying parameters are attenuated via asymptotic gain. Verification of asymptotic gain conditions is based on the relation between dissipation rates of unmeasured dynamics and timing characterizations ${mmbtau}_{bf p}$ and ${mmb T}_{bf p}$ of switching sequences.      

离散时间多智能体系统一致性的平均驻留时间条件

研究高阶离散时间线性多智能体系统在有向切换信息拓扑下的状态一致性问题。首先通过提出的线性变换将该一致性问题转换为相应离散时间线性切换系统的渐近稳定性问题。然后借助于切换系统稳定性的平均驻留时间方法,分别得到如下两种情形下该一致性问题可解的充分条件：1)信息拓扑集合中的一部分拓扑是可一致的;2)信息拓扑集合中所有信息拓扑是可一致的。最后通过数值仿真验证了所得理论结果的正确性。     

Decentralised output-feedback control design for switched fuzzy large-scale systems

This paper investigates the output-feedback control design problem for a class of switched Takagi–Sugeno fuzzy large-scale systems with non-measurable premise variables. The considered fuzzy large-scale systems consist of several interconnected subsystems with different switching modes and there exists the asynchronous switching between the system switching modes and the controller switching modes. A decentralised state observer is proposed to estimate the unmeasured states, and a new output-feedback decentralised control scheme is developed by using the state observers and the switching functions. Based on the theory of Lyapunov stability and average dwell-time methods, the sufficient conditions of ensuring the switched control system stability are proposed and proved, which are formulated in the form of linear matrix inequalities. An applicable example is provided to show the effectiveness of the obtained theoretical results.     

Switched nonlinear systems with state-dependent dwell-time

The asymptotic convergence of a switched nonlinear system in the presence of disturbances is studied. The system switches among a family of integral input-to-state stable systems. The time between two consecutive switchings is not less than a value τ_D. This dwell-time τ_D is allowed to take different values according to a function whose argument is the state of the system at the switching times. We propose a dwell-time function which depends on the comparison functions which characterize the integral input-to-state stability property and guarantees the state of the switched system to converge to zero under the action of disturbances with “bounded energy”. The main feature of the analysis is that it does not rely on the property for the switching to stop in finite time. The two important cases of locally exponentially stable and feedforward systems are analyzed in detail.     

Frequency-domain L 2-stability conditions for switched linear and nonlinear SISO systems

We consider the L ₂-stability analysis of single-input–single-output (SISO) systems with periodic and nonperiodic switching gains and described by integral equations that can be specialised to the form of standard differential equations. For the latter, stability literature is mostly based on the application of quadratic forms as Lyapunov-function candidates which lead, in general, to conservative results. Exceptions are some recent results, especially for second-order linear differential equations, obtained by trajectory control or optimisation to arrive at the worst-case switching sequence of the gain. In contrast, we employ a non-Lyapunov framework to derive L ₂-stability conditions for a class of (linear and) nonlinear SISO systems in integral form, with monotone, odd-monotone and relaxed monotone nonlinearities, and, in each case, with periodic or nonperiodic switching gains. The derived frequency-domain results are reminiscent of (i) the Nyquist criterion for linear time-invariant feedback systems and (ii) the Popov-criterion for time-invariant nonlinear feedback systems with the Lur'e-type nonlinearity. Although overlapping with some recent results of the literature for periodic gains, they have been derived independently in essentially the Popov framework, are different for certain classes of nonlinearities and address some of the questions left open, with respect to, for instance, the synthesis of the multipliers and numerical interpretation of the results. Apart from the novelty of the results as applied to the dwell-time problem, they reveal an interesting phenomenon of the switched systems: fast switching can lead to stability, thereby providing an alternative framework for vibrational stability analysis.     

Stability analysis of switched stochastic systems

In this paper, for a class of switched stochastic (SS) systems, the moment stability (M-S) and sample path stability (SP-S) are investigated, respectively, and there are two main contributions. First, based on accurate estimations for the powers of solution of a special nonswitched stochastic (nSS) system, by employing the concepts of a Lyapunov function and describing the switching laws with the average dwell-time and the subsystems, three sufficiency theorems of p-th M-S are given for the SS systems. Then, for the SP-S of such systems, based on the results of p-th M-S, two sufficiency theorems are obtained for p>2 and p=2, respectively.     

Stability analysis of hybrid switched nonlinear singular time-delay systems with stable and unstable subsystems

The issue of exponential stability of a class of continuous-time switched nonlinear singular systems consisting of a family of stable and unstable subsystems with time-varying delay is considered in this paper. Based on the free-weighting matrix approach, the average dwell-time approach and by constructing a Lyapunov-like Krasovskii functional, delay-dependent sufficient conditions are derived and formulated to check the exponential stability of such systems in terms of linear matrix inequalities (LMIs). By checking the corresponding LMI conditions, the average dwell-time and switching signal conditions are obtained. This paper also highlights the relationship between the average dwell-time of the switched nonlinear singular time-delay system, its stability and the exponential convergence rate of differential and algebraic states. A numerical example shows the effectiveness of the proposed method.     

Simultaneous reduced-order control and fault detection for discrete-time switched systems with relaxed persistent dwell time regularity

This paper focuses on the problem of simultaneous control and fault detection (FD) for discrete-time switched systems. The main goal is to develop a control/detection unit (CDU) associated with a switching law to control the system and detect faults simultaneously. When the switched systems are with partial measurable states, we directly use these states to construct partial control and FD signals. Next, the reduced-order CDU is designed to generate the other control and FD signals. Compared with existing results based on full-order CDU, the proposed results lead to less conservatism and reduce design complexity. The switching law is constructed in the frame of persistent dwell time (PDT) switching. A novel switching number constraint condition is introduced, which further relaxes the restrictions on the dwell time of switching processes of PDT. The less restriction on dwell time degrades the performance requirement of each subsystem and upgrades the degree of freedom for switching law design. Based on the proposed results, a class of nonweighted performance indexes is introduced to characterize the fault sensitivity and robustness. Finally, the effectiveness of the proposed method is illustrated by an example.     

A moving switching sequence approach for nonlinear model predictive control of switched systems with state‐dependent switches and state jumps

In this paper, we propose an approach for real‐time implementation of nonlinear model predictive control (NMPC) for switched systems with state‐dependent switches called the moving switching sequence approach. In this approach, the switching sequence on the horizon moves to the present time at each time as well as the optimal state trajectory and the optimal control input on the horizon. We assume that the switching sequence is basically invariant until the first predicted switching time reaches the current time or a new switch enters the horizon. This assumption is reasonable in NMPC for systems with state‐dependent switches and reduces computational cost significantly compared with the direct optimization of the switching sequence all over the horizon. We update the switching sequence by checking whether an additional switch occurs or not at the last interval of the present switching sequence and whether the actual switch occurs or not between the current time and the next sampling time. We propose an algorithm consisting of two parts: (1) the local optimization of the control input and switching instants by solving the two‐point boundary‐value problem for the whole horizon under a given switching sequence and (2) the detection of an additional switch and the reconstruction of the solution taking into account the additional switch. We demonstrate the effectiveness of the proposed method through numerical simulations of a compass‐like biped walking robot, which contains state‐dependent switches and state jumps.     

Input-to-state stability of switched systems and switching adaptive control

In this paper we prove that a switched nonlinear system has several useful input-to-state stable (ISS)-type properties under average dwell-time switching signals if each constituent dynamical system is ISS. This extends available results for switched linear systems. We apply our result to stabilization of uncertain nonlinear systems via switching supervisory control, and show that the plant states can be kept bounded in the presence of bounded disturbances when the candidate controllers provide ISS properties with respect to the estimation errors. Detailed illustrative examples are included.     

Adaptive stabilization of a class of uncertain switched nonlinear systems with backstepping control

In this paper, we focus on the problem of adaptive stabilization for a class of uncertain switched nonlinear systems, whose non-switching part consists of feedback linearizable dynamics. The main result is that we propose adaptive controllers such that the considered switched systems with unknown parameters can be stabilized under arbitrary switching signals. First, we design the adaptive state feedback controller based on tuning the estimations of the bounds on switching parameters in the transformed system, instead of estimating the switching parameters directly. Next, by incorporating some augmented design parameters, the adaptive output feedback controller is designed. The proposed approach allows us to construct a common Lyapunov function and thus the closed-loop system can be stabilized without the restriction on dwell-time, which is needed in most of the existing results considering output feedback control. A numerical example and computer simulations are provided to validate the proposed controllers.