Switching Linear Systems Research Articles

Dwell-Time-Based Robust Stabilization and L₂–Gain Analysis for Asynchronously Switched Linear Systems With Actuator Saturation

Dwell-Time-Based Robust Stabilization and <i>L</i>₂–Gain Analysis for Asynchronously Switched Linear Systems With Actuator Saturation

Sustainable Operation and Management of a Dynamic Supply Chain under the Framework of a Community with a Shared Future for Mankind

The values of a community with a shared future for mankind include the views of common interests, sustainable development, and global governance. This article will fully consider introducing the value concept of a community with a shared future into the operation and management of dynamic supply chains. Based on the optimal information fusion mechanism of artificial intelligence, this article aims to examine the operation and management of dynamic supply chains within the framework of a community with a shared future for mankind. The core idea is to consider the common interests among enterprises, establish a global collaborative operation concept for upstream, midstream, and downstream enterprises, and achieve the goal of sustainable development. Firstly, a type of composite dynamic supply chain model is considered, in which the total inventory of each node in the supply chain is further subdivided into raw material inventory and finished product inventory. At the same time, we have considered factors such as the signing of procurement contracts between core enterprises and upstream enterprises, as well as the signing of supply contracts between core enterprises and downstream enterprises. Secondly, the static and dynamic monitoring information of the enterprise has been established. We use steady-state Kalman filtering theory to obtain dynamic reference signals for upstream enterprises, core enterprises, and downstream enterprises. Based on the optimal information fusion processing mechanism of artificial intelligence, the coefficient weighting method is used to obtain the optimal fusion signals of upstream enterprises, core enterprises, and downstream enterprises. Once again, through high-quality switching strategies, enterprises can achieve in-order switching, improve production efficiency, reduce downtime, enhance their competitiveness and responsiveness, and transform the dynamic supply chain, including order switching, into a discrete-time linear switching system for processing. Fourthly, sufficient conditions, robustness analysis results, and inventory control criteria for the solvability of dynamic supply chain H∞ with order switching are provided. Finally, data analysis is conducted using historical order information from three fruit companies to verify the validity and feasibility of the conclusions in this article and to improve the performance of the dynamic supply chain system. The research findings of this article enrich the exploration of the operation and management of dynamic supply chains and the construction of a community with a shared future for mankind.

State-of-Charge Estimation of Reconfigurable Supercapacitor

Abstract A large body of research has been done on state-of-charge (SOC) estimate of supercapacitors in the literature; most of the works have been on SOC estimation of individual supercapacitor units. Nonetheless, supercapacitors are usually linked to balancing circuits in real-world applications in order to remove inter-cell imbalances. The cells’ system dynamics shift to a new mode when the balancing circuit is turned on, making the SOC calculation techniques that are currently in use inappropriate. Our proposal in this research is a Kalman filtering-based reconfigurable supercapacitor balancing system SOC estimate method. By fusing a reconfigurable balancing circuit with the equivalent circuit model of supercapacitors, we create a linear switching systems model. The switching system’s discrete-time form is shown, and its observability is examined. With filter gains dynamically modified according to the system mode, a switching Kalman filter is intended to estimate the SOC of the switched system. The accuracy of SOC estimation is greatly improved by the suggested method when supercapacitors are in the balancing mode, as confirmed by the simulation results.

Interpolated Bumpless Transfer Control for Asynchronously Switched Linear Systems

Interpolated Bumpless Transfer Control for Asynchronously Switched Linear Systems

Simultaneous Stabilization of Second Order Linear Switched Systems Based on Superstability and D-Decomposition Technique

Simultaneous Stabilization of Second Order Linear Switched Systems Based on Superstability and D-Decomposition Technique

Simultaneous Stabilization of Second Order Linear Switched Systems Based on Superstability and D-Decomposition Technique

Simultaneous Stabilization of Second Order Linear Switched Systems Based on Superstability and D-Decomposition Technique

Bayesian Inference of Recurrent Switching Linear Dynamical Systems with Higher-Order Dependence

Many complicated dynamical events may be broken down into simpler pieces and efficiently described by a system that shifts among a variety of conditionally dynamical modes. Building on switching linear dynamical systems, we develop a new model that extends the switching linear dynamical systems for better discovering these dynamical modes. In the proposed model, the linear dynamics of latent variables can be described by a higher-order vector autoregressive process, which makes it feasible to evaluate the higher-order dependency relationships in the dynamics. In addition, the transition of switching states is determined by a stick-breaking logistic regression, overcoming the limitation of a restricted geometric state duration and recovering the symmetric dependency between the switching states and the latent variables from asymmetric relationships. Furthermore, logistic regression evidence potentials can appear as conditionally Gaussian potentials by utilizing the Pólya-gamma augmentation strategy. Filtering and smoothing algorithms and Bayesian inference for parameter learning in the proposed model are presented. The utility and versatility of the proposed model are demonstrated on synthetic data and public functional magnetic resonance imaging data. Our model improves the current methods for learning the switching linear dynamical modes, which will facilitate the identification and assessment of the dynamics of complex systems.

Finite-time Issue of Discrete-time Linear Switched Systems With Partial Finite-time Unstable Modes Based on an Inverse Weighted Switching Scheme

Finite-time Issue of Discrete-time Linear Switched Systems With Partial Finite-time Unstable Modes Based on an Inverse Weighted Switching Scheme

A Stability Dichotomy for Discrete-Time Linear Switching Systems in Dimension Two

A Stability Dichotomy for Discrete-Time Linear Switching Systems in Dimension Two

Almost sure stability criteria for linear Markovian switching systems

We present some stability criteria mainly for continuous-time Markovian switching systems, which can provide us with an insight into the mechanism that drives the subsystems to interact with each other so as to achieve stability. On the one hand, directly computing the Lyapunov exponent through the state-transition matrix of the system under consideration allows us to capture the interaction of subsystems by using the method developed in discrete-time setting. On the other hand, we can make sense of how the subsystems are orchestrated by the statistical property of switching signal through a family of coupled Lyapunov inequalities, which naturally covers the stability in the mean-square sense as a special case. Three examples are included to illustrate the theoretical results.

Stability analysis of switching systems with all modes unstable based on a $ \Phi $-dependent max-minimum dwell time method

&lt;abstract&gt;&lt;p&gt;This paper applies stable and unstable switching instants to study switching systems with unstable modes under time-dependent switching signals. A new Lyapunov function is proposed to study the properties of switching instant using different $ \Phi $-dependent max-minimum dwell time methods. After that, the global exponential stability conditions for nonlinear and linear switching systems are derived and stable switching is used to compensate for unstable switching and unstable modes. The relevant results are extended to the controller design of linear switching systems. Finally, a simulation verifies the effectiveness of the results of this paper.&lt;/p&gt;&lt;/abstract&gt;

Analysis of Discrete-Time Switched Linear Systems Under Logical Dynamic Switching.

The control properties of discrete-time switched linear systems (SLSs) with switching signals generated by logical dynamical systems are studied using the semitensor product (STP) approach. With the algebraic state-space representation (ASSR), the linear modes and the logical generators are aggregated as a system with hybrid states, leading to the criteria of reachability, controllability, observability, and reconstructibility of the SLSs. Algorithms for checking these properties are given. Then, two kinds of realization problems concerning whether the logical dynamical systems can generate the desired switching signals are investigated, and necessary and sufficient conditions for the realizability of the desired switching signals are given with respect to the cases of fixed operating time (FOT) switching and finite reference signal switching.

Toward Stochastic Realization Theory for Generalized Linear Switched Systems With Inputs: Decomposition Into Stochastic and Deterministic Components and Existence and Uniqueness of Innovation Form

Toward Stochastic Realization Theory for Generalized Linear Switched Systems With Inputs: Decomposition Into Stochastic and Deterministic Components and Existence and Uniqueness of Innovation Form

Robust Model Predictive Control for Asynchronously Switched Linear Systems with Intermittent Controller Failures

Robust Model Predictive Control for Asynchronously Switched Linear Systems with Intermittent Controller Failures

Hierarchy of Quadratic Lyapunov Functions for Linear Time-Varying and Related Systems

A method for constructing homogeneous polynomial Lyapunov functions is presented for linear time-varying or switched-linear systems and the class of nonlinear systems that can be represented as such. The method uses a simple recursion based on the Kronecker product to generate a hierarchy of related dynamical systems, whose first element is the system under study and the second element is the well-known Lyapunov differential equation. It is then proven that a quadratic Lyapunov function for the system at one level in the hierarchy, which can be found via semidefinite programming, is a homogeneous polynomial Lyapunov function for the system at the base level in the hierarchy. Searching for Lyapunov functions of the foregoing kind is equivalent to searching for homogeneous polynomial Lyapunov functions via the formulation of sum-of-squares programs. The quadratic perspective presented in this paper enables the easy development of procedures to compute bounds on pointwise-in-time system metrics, such as peak norms, system stability margins, and many other performance measures. The applications of the theory to analyzing an aircraft model, on the one hand, and an experimental aerospace vehicle, on the other hand, are presented. The theory can be comprehended with a first course on state-space control systems and an elementary knowledge of convex programming.

Mode-Independent Switching Stabilizing Control for Continuous-Time Linear Markovian Switching Systems

We present a switching control approach to studying the stabilization problem of linear Markovian switching systems. The switching signal in feedback loop is generated independently of the underlying switching signal. Moreover, the closed-loop switching signal can be accelerated to show the influence of its stationary distribution. As a result, the transition matrix of the closed-loop system approximates such an operator semigroup that its infinitesimal generator exactly is the combination of the closed-loop subsystem matrices with respect to this stationary distribution. Therefore, endowing this infinitesimal generator with certain stable structure may allow us to make the closed-loop system exponentially stable at the expense of fast switching speed.

Fault Detection Problems for Switching Linear Systems: A Structural Approach

The fault detection and isolation problem is considered in the context of switching linear systems. The problem is tackled by searching for suitable residual signal generators, whose existence is completely characterized in structural terms. Both the situation in which the initial condition of the system subject to possible faults is known and that in which it is not known are considered. The results are compared with those found in the classical linear case for the same problem using a structural geometric approach in order to show consistency and to highlight differences.

Joint Estimation of Continuous and Discrete States in Randomly Switched Linear Systems With Unobservable Subsystems

Joint Estimation of Continuous and Discrete States in Randomly Switched Linear Systems With Unobservable Subsystems

Approximate moving horizon estimation for switching conservative linear infinite-dimensional systems

This work addresses moving horizon estimation for switching conservative linear infinite-dimensional systems described by partial differential equations (PDE), where the plant and measurement equations are corrupted with bounded disturbances, and the system mode is regarded as an unknown and unpredictable discrete state to be estimated. To address the issues associated with unbounded operators (induced by boundary or point observation and disturbance) and facilitate discrete-time moving horizon estimator design, the Cayley–Tustin transformation is deployed for model time-discretization without any spatial discretization or model reduction while preserving model essential properties. A series of observability concepts along with corresponding properties are proposed and analyzed for the switching linear infinite-dimensional discrete-time systems. A moving horizon estimation algorithm that accounts for state/output and mode estimation and constraint handling is proposed. Based on the proposed observability properties, we prove the stability of the proposed moving horizon estimator. The derived results are demonstrated by an undamped Schrödinger equation with switching group-velocity dispersion.

Controllability, reachability, observability performance analysis of ultra‐high voltage converter cascaded systems based on switched linear system model

SummaryUltra‐high voltage converters are usually employed to transform low voltage to high voltage in microgrids to produce renewable energy. However, it is challenging to develop control techniques due to the complicated structure of ultra‐high voltage converters and the numerous power switches and circuit components, which leads to poor dynamic characteristics of the system and a marked increase in fault rates. In order to understand the control theoretical characteristics of the ultra‐high voltage converter and provide a theoretical basis for circuit parameter analysis and control strategy design, this paper takes the boost converter cascaded system as an example to establish an accurate switching linear system model, discusses the control theoretical characteristics of the ultra‐high voltage converter in detail, and uses the decision theorem to draw the conclusion that the system is structurally controllable, reachable, and observable, simplifying the difficulty of analysis. The simulation and experimental findings show that the conclusion was drawn correctly. The research findings will give the boost converter cascaded systems modulation approach and circuit parameter design a theoretical foundation.