Convex conditions for robust stabilization of uncertain switched systems with guaranteed minimum dwell-time
Corentin Briat
本文针对具有保证最小驻留时间的不确定切换系统，提出基于凸条件的鲁棒镇定方法。
论文已被作者撤回。
Paper withdrawn by the author
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Affine characterizations of minimum and mode-dependent dwell-times for uncertain linear switched systems
本文提出一种基于Lyapunov循环泛函的仿射方法，用于刻画不确定线性切换系统的最小和模式依赖驻留时间，通过无限维LMI条件实现稳定性分析。
Stability analysis and stabilization of stochastic linear impulsive, switched and sampled-data systems under dwell-time constraints
本文研究了在驻留时间约束下随机线性冲击、切换和采样数据系统的稳定性分析与镇定问题，提出基于均方稳定性与驻留时间的概念，推导出适用于鲁棒分析与控制设计的凸时钟依赖线性矩阵不等式条件，并应用于随机采样数据系统的分析与控制。
This paper deals with the stability analysis problem of discrete-time switched linear systems with ranged dwell time. A novel concept called L-switching-cycle is proposed, which contains sequences of multiple activation cycles satisfying the prescribed ranged dwell time constraint. Based on L-switching-cycle, two sufficient conditions are proposed to ensure the global uniform asymptotic stability of discrete-time switched linear systems. It is noted that two conditions are equivalent in stability analysis with the same $L$-switching-cycle. These two sufficient conditions can be viewed as gener…
We propose an extension of the theory of control sets to the case of inputs satisfying a dwell-time constraint. Although the class of such inputs is not closed under concatenation, we propose a suitably modified definition of control sets that allows to recover some important properties known in the concatenable case. In particular we apply the control set construction to dwell-time linear switched systems, characterizing their maximal Lyapunov exponent looking only at trajectories whose angular component is periodic. We also use such a construction to characterize supports of invariant measur…
Switched Optimal Control with Dwell Time Constraints
针对带驻留时间约束的切换最优控制问题，本文在 MEOCP 基础上引入过滤层剔除违规切换，并用插入梯度降低其对最优代价的影响。
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。
Dwell-time stability and stabilization conditions for linear positive impulsive and switched systems
本文研究了线性脉冲正系统在不同驻留时间下的稳定性与镇定条件，通过线性Copositive Lyapunov函数提出稳定性条件，并采用提升方法将其转化为线性规划问题，进一步扩展到切换系统。
This paper presents an efficient suboptimal model predictive control (MPC) algorithm for nonlinear switched systems subject to minimum dwell time constraints (MTC). While MTC are required for most physical systems due to stability, power and mechanical restrictions, MPC optimization problems with MTC are challenging to solve. To efficiently solve such problems, the on-line MPC optimization problem is decomposed into a sequence of simpler problems, which include two nonlinear programs (NLP) and a rounding step, as typically done in mixed-integer optimal control (MIOC). Unlike the classical appr…
Practical Stabilization of Switched Affine Systems under Dwell Time: From Polytopic to p-Norm Lyapunov Functions
本文针对切换仿射系统在驻留时间约束下，提出基于加权p-范数李雅普诺夫函数的两步构造方法，实现期望工作点的实用渐近稳定，并推广了二次李雅普诺夫方法。
An Efficient Mixed-Integer Formulation and an Iterative Method for Optimal Control of Switched Systems Under Dwell Time Constraints
针对驻留时间约束下的离散控制切换系统，提出将问题分解为序列优化与切换时间优化的低二元变量MINLP建模，并辅以启发式迭代算法，在四类系统上验证了求解效率。
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。
Observer-Based Sampled-Data Stabilisation of Switched Systems with Lipschitz Nonlinearities and Dwell-Time
研究了具有不确定Lipschitz非线性的线性仿射切换系统在驻留时间约束下的稳定化问题，采用基于状态观测器的采样数据切换律，利用Lyapunov-Metzler不等式设计切换律，推导了闭环系统全局渐近稳定性的时变LMI条件，并讨论了LMI的可行性。
Generalized switching signals for input-to-state stability of switched systems
本文研究了连续时间切换非线性系统输入到状态稳定性问题，提出了一类新的通用切换信号，使切换系统具备ISS性质，并扩展了平均驻留时间切换信号的定义。
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…
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。
This paper is concerned with the problem of robust reliable control for a class of uncertain 2D discrete switched systems with state delays represented by a model of Roesser type. The parameter uncertainties are assumed to be norm-bounded. Firstly, delay-dependent sufficient condition for the exponential stability of the discrete 2D systems with state delays is established. Then, the concept of average dwell time is extended to 2D switched systems, and a reliable state feedback controller is developed in terms of linear matrix inequalities (LMIs) such that the resulting closed-loop system is e…
Simple interval observers for linear impulsive systems with applications to sampled-data and switched systems
本文提出了一种简单区间观测器的设计方法，用于满足最小和范围驻留时间约束的线性脉冲系统，并通过三个示例展示了其在采样数据和切换系统中的应用。
Towards a Global Controller Design for Guaranteed Synchronization of Switched Chaotic Systems
本文基于保证稳定性Lyapunov理论，结合鲁棒控制与切换线性系统概念，推导出切换主从非线性混沌系统的同步充分条件，并通过线性矩阵不等式简化计算以实现同步控制。
Stabilization of 2D discrete switched systems with state delays under asynchronous switching
针对控制器切换滞后于系统切换的异步切换问题，采用驻留时间方法设计状态反馈控制器，实现具有状态时滞和范数有界不确定性的Roesser型二维离散切换系统的鲁棒指数镇定。
Quantized Output Feedback Stabilization of Switched Linear Systems
本文研究通过量化输出反馈稳定连续时间切换线性系统，利用多Lyapunov函数和平均驻留时间性质设计编码策略，并在每次切换时调整'缩放'参数。
Switched linear hyperbolic partial differential equations are considered in this paper. They model infinite dimensional systems of conservation laws and balance laws, which are potentially affected by a distributed source or sink term. The dynamics and the boundary conditions are subject to abrupt changes given by a switching signal, modeled as a piecewise constant function and possibly a dwell time. By means of Lyapunov techniques some sufficient conditions are obtained for the exponential stability of the switching system, uniformly for all switching signals. Different cases are considered w…
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。
This paper proposes a unified approach for studying global exponential stability of a general class of switched systems described by time-varying nonlinear functional differential equations. Some new delay-independent criteria of global exponential stability are established for this class of systems under arbitrary switching which satisfies some assumptions on the average dwell time. The obtained criteria are shown to cover and improve many previously known results, including, in particular, sufficient conditions for absolute exponential stability of switched time-delay systems with sector non…
Switched linear systems are time-varying nonlinear systems whose dynamics switch between different modes, where each mode corresponds to different linear dynamics. They arise naturally to model unexpected failures, environment uncertainties or system noises during system operation. In this paper, we consider a special class of switched linear systems where the mode switches are governed by Markov decision processes (MDPs). We study the problem of synthesizing a policy in an MDP that stabilizes the switched system. Given a policy, the switched linear system becomes a Markov jump linear system w…
Convex lifted conditions for robust stability analysis and stabilization of linear discrete-time switched systems
本文提出基于凸LMI条件的离散时间切换系统在最小驻留时间下的稳定性分析与控制方法，通过提升过程将非凸条件转化为凸条件，有效扩展至不确定系统、控制设计和ℓ₂增益计算。
In this paper, we study the application of switched systems stability criteria to derive delay-dependent conditions for systems affected by both a constant and a time-varying delay. The main novelty of our approach lies on the use of path-complete Lyapunov techniques along with the proposition of a new modified functional to obtain convex analysis conditions while avoiding the need of computing a dwell time for each mode in a switched system representation, as usual in the \textit{switched approach} for time-delay systems. Furthermore, we leverage the developed analysis to obtain LMIs for the …
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。
Guaranteed Fault Detection and Isolation for Switched Affine Models
本文研究切换仿射模型的故障检测与隔离问题，提出基于优化的新型方法，提高计算效率，并引入区分度指数用于确定故障检测时间窗和设计建议，进一步扩展到多故障模型的故障隔离，提出高效实现方案并减少隔离延迟。
Linear Programming based Lower Bounds on Average Dwell-Time via Multiple Lyapunov Functions
针对切换系统平均驻留时间最小下界求解难的问题，将非凸优化转化为线性规划问题，基于多Lyapunov函数给出指数稳定性下界，实验验证较现有方法有提升。
In this paper, we study the problem of stabilizing switched linear systems when only limited information about the state and the mode of the system is available, which occurs in many applications involving networked switched systems (such as cyber-physical systems, IoT, etc.). First, we show that switched linear systems with arbitrary switching, i.e., with no constraint on the switching signal, are in general not stabilizable with a finite data rate. Then, drawing on this result, we restrict our attention to systems satisfying a fairly mild slow-switching assumption, in the sense that the swit…
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。
Adaptive Control of Unknown Linear Switched Systems via Policy Gradient Methods
本文提出了一种基于策略梯度的方法，用于稳定未知参数和切换时间的线性切换系统，通过滑动窗口数据实现闭环稳定性。
Stability and $L_1/\ell_1$-to-$L_1/\ell_1$ performance analysis of uncertain impulsive linear positive systems with applications to the interval observation of impulsive and switched systems with constant delays
本文研究了具有恒定延迟的脉冲和切换系统的区间观测问题，通过构建线性分数形式的不确定线性脉冲正系统稳定性及$L_1/\ell_1$-到$L_1/\ell_1$性能分析条件，利用时间变化的$D$-缩放参数，提出了范围和最小驻留时间条件，并将这些条件转化为无限维线性规划问题，通过多项式优化技术转化为有限维问题。同时，展示了在某些条件下，缩放参数可以被消除，从而得到等价的“最坏情况系统”稳定性条件。最后，将该方法应用于具有延迟的线性正系统，并考虑了切换系统延迟的情况。
Stability analysis and stabilization of LPV systems with jumps and (piecewise) differentiable parameters using continuous and sampled-data controllers
本文针对具有跳跃和分段可微参数的混合LPV系统，提出基于时钟和参数依赖Lyapunov函数的方法，推导出在常数和最小驻留时间下的稳定性条件，并通过时依赖和时/参数无关状态反馈控制器实现镇定。
This paper is concerned with the study of both, local and global, uniform asymptotic stability for switched nonlinear time-varying (NLTV) systems through the detectability of output-maps. With this aim the notion of reduced limiting control systems for switched NLTV systems whose switchings verify time/state dependent constraints, and the concept of weakly zero-state detectability for those reduced limiting systems are introduced. Necessary and sufficient conditions for the (global)uniform asymptotic stability of families of trajectories of the switched system are obtained in terms of this det…
$L_1/\ell_1$-to-$L_1/\ell_1$ analysis of linear positive impulsive systems with application to the $L_1/\ell_1$-to-$L_1/\ell_1$ interval observation of linear impulsive and switched systems
本文研究了在线性正脉冲系统中，基于最小和范围驻留时间约束的渐近稳定性和混合$L_1/\ell_1$增益的充分条件，并将其转化为无限维线性规划问题，通过求和平方规划进行求解。这些条件被用于构建线性脉冲和切换系统的$L_1/\ell_1$到$L_1/\ell_1$区间观测器的构造性充分条件，通过求解无限维优化问题提取合适的观测器增益，并通过示例进行说明。
Recent works have shown that the $L_1$ and $L_\infty$-gains are natural performance criteria for linear positive systems as they can be characterized using linear programs. Those performance measures have also been extended to linear positive impulsive and switched systems through the concept of hybrid $L_1\times\ell_1$-gain. For LTI positive systems, the $L_\infty$-gain is known to coincide with the $L_1$-gain of the transposed system and, as a consequence, one can use linear copositive Lyapunov functions for characterizing the $L_\infty$-gain of LTI positive systems. Unfortunately, this does…
Data-driven mode detection and stabilization of unknown switched linear systems
本文研究未知切换线性系统的数据驱动稳定化问题，基于线性矩阵不等式设计在线切换控制器，通过在线测量进行模式检测与稳定化，在平均驻留时间假设下保证闭环系统的实际稳定性。
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 …
A design framework recently has been developed to stabilize interconnected multiagent systems in a distributed manner, and systematically capture the architectural aspect of cyber-physical systems. Such a control theoretic framework, however, results in a stabilization protocol which is passive with respect to the cyber attacks and conservative regarding the guaranteed level of resiliency. We treat the control layer topology and stabilization gains as the degrees of freedom, and develop a mixed control and cybersecurity design framework to address the above concerns. From a control perspective…
This paper deals with an event-triggered boundary control of constant-parameters reaction-diffusion PDE systems. The approach relies on the emulation of backstepping control along with a suitable triggering condition which establishes the time instants at which the control value needs to be sampled/updated. In this paper, it is shown that under the proposed event-triggered boundary control, there exists a minimal dwell-time (independent of the initial condition) between two triggering times and furthermore the well-posedness and global exponential stability are guaranteed. The analysis follows…
Uniform Exponential Stability Analysis of Impulsive Linear Time-Invariant Systems on Banach and Hilbert Spaces: Non-Coercive and Coercive Stability Conditions
研究无限维脉冲系统在巴拿赫和希尔伯特空间上的一致指数稳定性分析，结合混合系统与无限维系统思想得出基于算子的稳定性条件，给出充要条件，应用于线性切换系统，通过理论和数值示例说明，尤其用于时滞系统采样数据控制。
We analyze robust stability, in an input-output sense, of switched stable systems. The primary goal (and contribution) of this paper is to design switching strategies to guarantee that input-output stable systems remain so under switching. We propose two types of {\em supervisors}: dwell-time and hysteresis based. While our results are stated as tools of analysis they serve a clear purpose in design: to improve performance. In that respect, we illustrate the utility of our findings by concisely addressing a problem of observer design for Lur'e-type systems; in particular, we design a hybrid ob…
This paper provides observer-based sampled-data and event-triggered boundary control strategies for a class of reaction-diffusion PDEs with collocated sensing and Robin actuation. Infinite-dimensional backstepping design is used as the underlying control approach. It is shown that the continuous-time output feedback boundary control applied in a sample-and-hold fashion ensures global closed-loop exponential stability, provided that the sampling period is sufficiently small. Further, robustness to perturbations of the sampling schedule is guaranteed. For the event-triggered implementation of th…
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