我们提出了一种编码和控制策略，用于有限信息下的切换系统稳定化，假设每个模式都有给定的控制器。仅在每个采样时间将量化输出和植物的主动模式传输给控制器。由于切换，植物的主动模式可能与闭环系统中的控制器不同。因此，如果发生切换，则量化器必须在下一个采样时间重新计算一个包含量化误差估计的有界集。我们基于慢切换假设（ dwell time 和 average dwell time）建立了全局渐近稳定性。为此，我们构造了多个离散时间Lyapunov函数，分别针对估计状态和有界集的大小。
英文摘要：
We propose an encoding and control strategy for the stabilization of switched systems with limited information, supposing the controller is given for each mode. Only the quantized output and the active mode of the plant at each sampling time are transmitted to the controller. Due to switching, the active mode of the plant may be different from that of the controller in the closed-loop system. Hence if switching occurs, the quantizer must recalculate a bounded set containing the estimation error for quantization at the next sampling time. We establish the global asymptotic stability under a slow-switching assumption on dwell time and average dwell time. To this end, we construct multiple discrete-time Lyapunov functions with respect to the estimated state and the size of the bounded set.
Feedback stabilization of switched systems under arbitrary switching: A convex characterization
Aeronautics Institute of Technology (ITA)（巴西空军理工学院）；Politecnico di Torino（都灵理工大学）；Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire des Signaux et Systèmes（巴黎萨克雷大学、法国国家科学研究中心、中央苏佩莱克学院、信号与系统实验室）
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 …
Practical Stabilization of Switched Affine Systems under Dwell Time: From Polytopic to p-Norm Lyapunov Functions
Centro Internacional Franco-Argentino de Cs. de la Información y de Sistemas (CIFASIS), UNR–CONICET（中法阿根廷信息与系统国际中心（CIFASIS），罗萨里奥国立大学-国家科学研究委员会）；Military Institute of Engineering（军事工程学院）
This survey paper deals with the stabilization of nonlinear systems by analyzing the controlling method in terms of state feedback and output feedback. A brief overview of some literature on how the feedback controller of some dynamic systems in real applications like robots can be applicable is introduced. The aim is to give a direction about the methods of how to solve the state and output feedback stabilization problems for nonlinear systems based on feedback design methods and other theorems like the Lyapunov stability theorem. The feedback controllers can be constructed to ensure the orig…
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…
In this paper, we address the global stabilization of chains of integrators by means of a bounded static feedback law whose p first time derivatives are bounded. Our construction is based on the technique of nested saturations introduced by Teel. We show that the control amplitude and the maximum value of its p first derivatives can be imposed below any prescribed values. Our results are illustrated by the stabilization of the third order integrator on the feedback and its first two derivatives.
This note studies the robust output feedback stabilization problem of a class of multi-input multi-output invertible nonlinear systems, for which an "ideal" state feedback based on feedback linearization can be designed under certain mild assumptions. By systematically designing a set of extended low-power high-gain observers, we show that this "ideal" linearizing feedback law can be approximately estimated, which provides a robust output feedback stabilizer such that the origin of the resulting closed-loop system is semiglobally asymptotically stable.
Stability and control of a non-linear system represent an important system configuration that frequently arises in practical engineering. Stability covers a vast range of systems that do not obey the superposition principle and applies to more real-world systems because all real control systems are non-linear. For efficient stabilization of these systems, a great number of researches have been proposed. This paper surveys some well-known facts as well as some recent developments and different strategies for the topic of stabilization of non-linear systems by output feedback control techniques.
This note studies the robust output feedback stabilization problem of multi-input multi-output invertible nonlinear systems with output-dependent multipliers. An "ideal" state feedback is first designed under certain mild assumptions. Then, a set of extended low-power high-gain observers is systematically designed, providing a complete estimation of the "ideal" feedback law. This yields a robust output feedback stabilizer such that the origin of the closed-loop system is semiglobally asymptotically stable, while improving the numerical implementation with the power of high-gain parameters up t…
The stabilization of unstable nonlinear systems and tracking control are challenging engineering problems due to the encompassed nonlinearities in dynamic systems and their scale. In the past decades, numerous observer-based control designs for dynamic systems in which the nonlinearity belongs to Lipschitz functions have been proposed. However, most of them only focus on output feedback and consequently, state feedback design remains less developed. To that end, this paper is dedicated to the problem of full-state feedback controller design for discrete-time Lipschitz nonlinear systems. In add…
Internal oscillations in switched antenna transmitters cause undesirable fluctuations of the stored energy in the system, reducing the effectiveness of time-varying broadbanding methods, such as energy-synchronous direct antenna modulation. To mitigate these parasitic oscillations, a modified direct antenna modulation system with an auxiliary DC source is introduced to stabilize energy storage on the antenna. A detailed circuit model for a direct antenna modulation system is used to identify the origin of the oscillations and to justify the selection of the DC source. Measured phase shift keye…
Indian Institute of Science Bangalore（印度科学理工学院班加罗尔）
This paper deals with stabilization of discrete-time switched linear systems when explicit knowledge of the state-space models of their subsystems is not available. Given the set of admissible switches between the subsystems, the admissible dwell times on the subsystems and a set of finite traces of state trajectories of the subsystems that satisfies certain properties, we devise an algorithm that designs periodic switching logics which preserve stability of the resulting switched system. We combine two ingredients: (a) data-based stability analysis of discrete-time linear systems and (b) mult…
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 …
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…
In this note we study the generation of attractive oscillations of a class of mechanical systems with underactuation one. The proposed design consists of two terms, i.e., a partial linearizing state feedback, and an immersion and invariance orbital stabilization controller. The first step is adopted to simplify analysis and design, however, bringing an additional difficulty that the model loses its Euler-Lagrange structure after the collocated pre-feedback. To address this, we propose a constructive solution to the orbital stabilization problem via a smooth controller in an analytic form, and …
This paper studies the boundary output feedback stabilization of general 1-D reaction-diffusion PDEs in the presence of a state delay in the reaction term. The control input applies through a Robin boundary condition while the system output is selected as a either Dirichlet or Neumann boundary trace. The control strategy takes the form of a finite-dimensional observer-based controller with feedback and observer gains that are computed in order to dominate the state delayed term. For any arbitrarily given value of the state delay, we show the exponential stability of the resulting closed-loop s…
This paper addresses the topic of global output feedback stabilization of semilinear reaction-diffusion PDEs. The semilinearity is assumed to be confined into a sector condition. We consider two different types of actuation configurations, namely: bounded control operator and right Robin boundary control. The measurement is selected as a left Dirichlet trace. The control strategy is finite dimensional and is designed based on a linear version of the plant. We derive a set of sufficient conditions ensuring the global exponential stabilization of the semilinear reaction-diffusion PDE. These cond…
This paper discusses the boundary feedback stabilization of a reaction-diffusion equation with Robin boundary conditions and in the presence of a time-varying state-delay. The proposed control design strategy is based on a finite-dimensional truncated model obtained via a spectral decomposition. By an adequate selection of the number of modes of the original infinite-dimensional system, we show that the design performed on the finite-dimensional truncated model achieves the exponential stabilization of the original infinite-dimensional system. In the presence of distributed disturbances, we sh…
This paper is concerned with the output feedback stabilization of a reaction-diffusion equation by means of bounded control inputs in the presence of saturations. Using a finite-dimensional controller composed of an observer coupled with a finite-dimensional state-feedback, we derive a set of conditions ensuring the stability of the closed-loop plant while estimating the associated domain of attraction in the presence of saturations. This set of conditions is shown to be always feasible for an order of the observer selected large enough. The stability analysis relies on Lyapunov functionals al…
