Jesus San Martin, Anthony G. O'Farrell
We report conditions on a switching signal that guarantee that solutions of a switched linear systems converge asymptotically to zero. These conditions are apply to continuous, discrete-time and hybrid switched linear systems, both those having stable subsystems and mixtures of stable and unstable subsystems.
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A switched equilibrium of a switched system of two subsystems is a such a point where the vector fields of the two subsystems point strictly towards one another. Using the concept of stable convex combination that was developed by Wicks-Peleties-DeCarlo (1998) for linear systems, Bolzern-Spinelli (2004) offered a design of a state feedback switching rule that is capable to stabilize an affine switched system to any switched equilibrium. The state feedback switching rule of Bolzern-Spinelli gives a nonlinear (quadratic) switching threshold passing through the switched equilibrium. In this paper…
This paper deals with input/output-to-state stability (IOSS) of switched nonlinear systems in the discrete-time setting. We present an algorithm to construct periodic switching signals that obey pre-specified restrictions on admissible switches between the subsystems and admissible dwell times on the subsystems, and identify sufficient conditions on the individual subsystems, the admissible switches and admissible dwell times under which a switching signal obtained from our algorithm preserves stability of a switched system with overwhelming probability. We recover our earlier result on probab…
This article is concerned with stability analysis and stabilization of randomly switched systems under a class of switching signals. The switching signal is modeled as a jump stochastic (not necessarily Markovian) process independent of the system state; it selects, at each instant of time, the active subsystem from a family of systems. Sufficient conditions for stochastic stability (almost sure, in the mean, and in probability) of the switched system are established when the subsystems do not possess control inputs, and not every subsystem is required to be stable. These conditions are employ…
In this paper we consider switched nonlinear systems under average dwell time switching signals, with an otherwise arbitrary compact index set and with additional constraints in the switchings. We present invariance principles for these systems and derive by using observability-like notions some convergence and asymptotic stability criteria. These results enable us to analyze the stability of solutions of switched systems with both state-dependent constrained switching and switching whose logic has memory, i.e., the active subsystem only can switch to a prescribed subset of subsystems.
Mean uniformly stable function and its application to almost sure stability analysis of randomly switched time-varying systems
针对随机切换时变系统的一致几乎必然稳定性分析问题，提出均值一致稳定函数（MUSF）条件，结合不定多Lyapunov函数（iMLFs）构建概率视角的稳定判据，可适配含不稳定或非指数衰减子系统的场景，经数值算例验证有效。
Converse Lyapunov Results for Stability of Switched Systems with Average Dwell-Time
本文研究平均驻留时间约束下切换非线性系统的稳定性，通过反例区分驻留时间与平均驻留时间，并给出不依赖子系统流、更易检验的多 Lyapunov 函数充要条件。
Feedback rectifiable pairs and stabilization of switched linear systems
本文提出了一种针对切换线性系统稳定化的方法，通过反馈可修正对矩阵对，设计具有相同特征结构的闭环子系统以实现任意切换下的稳定性。
Compositional Construction of Barrier Functions for Switched Impulsive Systems
针对高维切换脉冲系统安全验证难题，本文提出通过为各子系统构造局部障碍函数并组合得到全局安全保证的充分条件，并在流行病学模型上验证了有效性。
Robust matrix commutator conditions for stability of switched linear systems under restricted switching
本文研究了在限制切换下离散时间切换线性系统的全局均匀指数稳定性，通过矩阵交换条件提供子系统的充分稳定性条件，避免使用Lyapunov函数。
On stability and state-norm estimation of switched systems under restricted switching
本文研究连续时间切换非线性系统在受限切换下的IOSS分析与状态范数估计器构造，基于类Lyapunov函数识别出保持稳定性的切换信号类，并设计了含稳定与不稳定子系统的估计器。
The paper is concerned with asymptotic stability properties of linear switched systems. Under the hypothesis that all the subsystems share a non strict quadratic Lyapunov function, we provide a large class of switching signals for which a large class of switched systems are asymptotically stable. For this purpose we define what we call non chaotic inputs, which generalize the different notions of inputs with dwell time. Next we turn our attention to the behaviour for possibly chaotic inputs. To finish we give a sufficient condition for a system composed of a pair of Hurwitz matrices to be asym…
Data-driven feedback rectification of switched linear systems
针对切换线性系统，提出数据驱动方法计算稳定状态反馈以校正特征结构，使子系统有相同特征向量集，能计算共同二次李雅普诺夫函数确保闭环系统渐近稳定，通过实例进行了说明。
Yet another stability condition for switched nonlinear systems
本文针对含不稳定动力学的连续时间切换非线性系统，利用多个类Lyapunov函数，识别出满足切换与驻留时间约束且能保持系统输入/输出-状态稳定性的切换信号，ISS和GAS为其特例。
We investigate the uniform stability properties of discrete-time linear switched systems subject to arbitrary switching, focusing on the "marginally unstable" regime in which the system is not Lyapunov stable but in which trajectories cannot escape to infinity at exponential speed. For a discrete linear system of this type without switching the fastest-growing trajectory must grow as an exact polynomial function of time, and a significant body of prior research has focused on investigating how far this intuitive picture can be extended from systems without switching to cases where switching is…
On maximum hands-off restricted hybrid control for discrete-time switched linear systems
本文提出了一种新算法，用于设计离散时间切换线性系统在指定时间内最大无干扰的混合控制序列，通过图论和线性代数分析，结合数值示例验证了方法的有效性。
Evolutionary dynamics under periodic switching of update rules on regular networks
本文研究了规则网络上智能体周期性切换策略更新规则的演化囚徒困境博弈，开发了基于复制器方程的切换系统理论框架，证明了周期性切换系统收敛至全合作状态的理论条件，并通过数值计算验证了理论结果。
Switched Linear Ensemble Systems and Structural Controllability
本文研究了切换线性系统集合的结构可控性问题，提出了一种基于稀疏模式的可控性判定方法，并通过最大流算法实现了高效计算。
Topological Entropy Bounds for Switched Linear Systems with Lie Structure
本文研究了具有李结构的切换线性系统的拓扑熵界，通过分析标量切换情况下的熵计算，扩展到非标量线性时不变和非标量切换情况，利用矩阵可交换关系和子系统特征值提供熵上界。
This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic process which is independent of the state of the system, and between two consecutive switching instants the dynamics are deterministic. Our results provide sufficient conditions for almost sure global asymptotic stability using Lyapunov-based methods when individual subsystems are stable and a certain ``slow switching'' condition holds. This slow switching cond…
Parameter Estimation of Switched Hammerstein Systems
针对可在线观测切换律的SISO切换Hammerstein系统，通过引入“内在切换”概念并应用递推最小二乘算法，在两种激励条件下实现了参数估计的强一致性。
Structural Controllability of Switched Linear Systems
针对参数未知或为零的切换线性系统，利用图论方法提出两种图形表示，并给出结构可控性的充要条件。
In this paper, incremental exponential asymptotic stability of a class of switched Carathéodory nonlinear systems is studied based on the novel concept of measure of switched matrices via multiple norms and the transaction coefficients between these norms. This model is rather general and includes the case of staircase switching signals as a special case. Sufficient conditions are derived for incremental stability allowing for the system to be incrementally exponentially asymptotically stable even if some of its modes are unstable in some time periods. Numerical examples on switched linear sys…
Robust performance for switched systems with constrained switching and its application to weakly hard real-time control systems
本文提出了一个基于耗散性理论和线性矩阵不等式的框架，用于分析和设计具有约束切换的切换系统的鲁棒二次性能控制器，并成功应用于不确定弱硬实时控制系统。
For the identification of switched systems with a measured switching signal, this work aims to analyze the effect of switching strategies on the estimation error. The data for identification is assumed to be collected from globally asymptotically or marginally stable switched systems under switches that are arbitrary or subject to an average dwell time constraint. Then the switched system is estimated by the least-squares (LS) estimator. To capture the effect of the parameters of the switching strategies on the LS estimation error, finite-sample error bounds are developed in this work. The obt…
It is desirable but challenging to fulfill system constraints and reach optimal performance in consensus protocol design for practical multi-agent systems (MASs). This paper investigates the optimal consensus problem for general linear MASs subject to control input constraints. Two classes of MASs including subsystems with semi-stable and unstable dynamics are considered. For both classes of MASs without input constraints, the results on designing optimal consensus protocols are first developed by inverse optimality approach. Utilizing the optimal consensus protocols, the receding horizon cont…
Continuous-Time Constrained Linear Quadratic Regulator for Switched Linear Systems
针对切换线性系统的连续时间约束线性二次调节器问题，提出通过固定切换序列并优化区间持续时间来间接优化切换序列，推导代价函数及其梯度的解析表达式，实现高效优化并提升计算效率。
ISS Lyapunov Functions for Cascade Switched Systems and Sampled-Data Control
本文研究了级联连接的切换系统输入到状态稳定性问题，提出了用于级联块的ISS Lyapunov函数，并利用这些函数构建整体系统的ISS Lyapunov函数，同时分析了混合系统的稳定性并推导了平均驻留时间的下界。
We demonstrate the use of a new, control-oriented notion of finite state approximation for a particular class of hybrid systems. Specifically, we consider the problem of designing a stabilizing binary output feedback switching controller for a pair of unstable homogeneous second order systems. The constructive approach presented in this note, in addition to yielding an explicit construction of a deterministic finite state approximate model of the hybrid plant, allows us to efficiently establish a useable upper bound on the quality of approximation, and leads to a discrete optimization problem …
Non-overshooting output shaping for switched linear systems under arbitrary switching using eigenstructure assignment
本文提出了一种在任意切换下实现切换线性系统无超调输出跟踪的控制设计方法，通过特征结构分配确保系统稳定性并提供可行的子系统分配方案。
Stabilizing switching signals for switched linear systems
针对可能包含不稳定动态的连续时间切换线性系统，通过约束切换信号的渐近频率、激活比例和转移密度，利用多李雅普诺夫函数方法刻画了一类保证全局渐近稳定的切换信号。
Motivated by the goal of learning controllers for complex systems whose dynamics change over time, we consider the problem of designing control laws for systems that switch among a finite set of unknown discrete-time linear subsystems under unknown switching signals. To this end, we propose a method that uses data to directly design a control mechanism without any explicit identification step. Our approach is online, meaning that the data are collected over time while the system is evolving in closed-loop, and are directly used to iteratively update the controller. A major benefit of the propo…
Hybrid Control of ADT Switched Linear Systems subject to Actuator Saturation
本文提出了一种针对具有执行器饱和的ADT切换线性系统的混合输出反馈控制方法，通过死区表示处理饱和非线性，并结合模式依赖的动态输出反馈控制器与监督重置机制，确保系统在ADT切换下的指数稳定性与扰动衰减性能。
This paper treats the global stabilization problem of continuous-time switched affine systems that have rank-deficient convex combinations of their dynamic matrices. For these systems, the already known set of attainable equilibrium points has higher dimensionality than in the full-rank case due to the existence of what we define as singular equilibrium points. Our main goal is to design a state-dependent switching function to ensure global asymptotic stability of a chosen point inside this set with conditions expressed in terms of linear matrix inequalities. For this class of systems, global …
Commutator-Driven Stability Bounds for Periodic Switching
研究周期性切换线性系统，推导了切换与平均传播器单周期失配的算子范数界限，其误差取决于模式生成器的成对换向器范数，给出切换周期阈值，通过伸缩归纳扩展到任意模式，还提供了相关李雅普诺夫度量。
We study the following optimization problem over a dynamical system that consists of several linear subsystems: Given a finite set of $n\times n$ matrices and an $n$-dimensional vector, find a sequence of $K$ matrices, each chosen from the given set of matrices, to maximize a convex function over the product of the $K$ matrices and the given vector. This simple problem has many applications in operations research and control, yet a moderate-sized instance is challenging to solve to optimality for state-of-the-art optimization software. We propose a simple exact algorithm for this problem. Our …
Lyapunov Characterization for ISS of Impulsive Switched Systems
本研究提出两种时间变化ISS-Lyapunov函数，用于分析具有稳定和不稳定模式的脉冲切换系统的ISS特性，并提供构造递减函数的方法。
Stabilizing switching signals: a transition from point-wise to asymptotic conditions
本文研究了确保切换系统稳定的切换信号类别，提出了一种新的通用稳定切换信号类别，并证明了基于点wise和渐近条件的先前结果都遵循该结果，首次将这些切换信号统一在一个框架下。
This paper investigates requirements on a networked dynamic system (NDS) such that its subsystem interactions can be solely determined from experiment data or reconstructed from its overall model. The NDS is constituted from several subsystems whose dynamics are described through a descriptor form. Except regularity on each subsystem and the whole NDS, no other restrictions are put on either subsystem dynamics or subsystem interactions. A matrix rank based necessary and sufficient condition is derived for the global identifiability of subsystem interactions, which leads to several conclusions …
We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable subsystems with one-dimensional unstable dynamics or critically stable dynamics. Systems of this type arise in problems of nonlinear output regulation, parameter estimation and adaptive control. In addition to providing boundedness and convergence criteria the results allow to derive domains of initial conditions corresponding to solutions leaving a given neig…
Stable state and signal estimation in a network context
针对网络分层中未知互连信号导致的估计难题，研究同时输入和状态估计算法，通过内-外分解或高方差白信号模型改进，证明外因子估计与原系统渐近一致，实现无偏状态估计。
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