Arbitrary Switching Signals Research Articles

Stability of shuffled switched linear systems: A joint spectral radius approach

A switching signal for a switched system is said to be shuffled if all modes of the system are activated infinitely often. In this paper, we develop tools to analyze stability properties of discrete-time switched linear systems driven by shuffled switching signals. We introduce the new notion of shuffled joint spectral radius (SJSR), which intuitively measures how much the state of the system contracts each time the signal shuffles (i.e. each time all modes have been activated). We show how this notion relates to stability properties of the associated switched systems. In particular, we show that some switched systems that are unstable for arbitrary switching signals can be stabilized by using switching signals that shuffle sufficiently fast and that the SJSR allows us to derive an expression of the minimal shuffling rate required to stabilize the system. We then present several approaches to compute lower and upper bounds of the SJSR using tools such as the classical joint spectral radius, Lyapunov functions and finite state automata. Several tightness results of the bounds are established. Finally, numerical experiments are presented to illustrate the main results of the paper.

Robust stability of Switched Boolean Networks with function perturbation

In genetic regulatory networks, gene mutations are one of natural phenomena, which attract much attention by biological researchers. In modeling gene networks using switched Boolean networks (SBNs), gene mutations can be described by function perturbations, which is a meaningful issue in analyzing function perturbation of SBNs. This paper studies robust stability of SBNs with function perturbation. With the help of semi-tensor product (STP) of matrices, one equivalent algebraic form of SBNs is established. By constructing two state sets, a criterion for global stability of SBNs under arbitrary switching signals is proposed. In order to relax the conditions of global stability, pointwise stabilizability and consistent stabilizability of SBNs are further considered. Based on state reachable sets, several criteria are established for the proposed kinds of stability. Finally, the obtained results are verified by two examples and lac operon in the Escherichia coli, respectively.

Codesign method for event‐triggered control of a class of switched nonlinear systems

AbstractThis article investigates the stability problem of a class of switched nonlinear systems by using the codesign of the switching law, the output feedback controller and the static output feedback based dynamic event‐triggered control (ETC). Each subsystem of such switched systems is allowed to be uncontrollable. The codesign method can not only guarantee asymptotic stability of the origin but also exclude Zeno behavior even if none of subsystems of the closed‐loop systems is stable and the switching can lead to the triggers instantaneously. A sufficient condition of using the above codesign method to ensure asymptotic stability without Zeno behavior is given. In addition, sufficient conditions of using the codesign of the output feedback controller and the static output feedback based dynamic ETC under arbitrary switching signals with dwell time for guaranteeing asymptotic stability and the positive lower bound of the interexecution times are developed even if the switching can result in the triggers instantaneously and some closed‐loop subsystems are still unstable. Further, sufficient conditions of using the codesign method to guarantee asymptotic stability without Zeno behavior under arbitrary switching signals with average dwell time are also developed. Finally, a numerical example is given to illustrate the effectiveness of the results.

Adaptive tracking control of time‐varying delay switched nonstrict‐feedback nonlinear systems with unknown backlash‐like hysteresis

SummaryIn this article, the adaptive tracking control issue is addressed for uncertain switched nonstrict‐feedback nonlinear systems with unknown time‐varying delay and backlash‐like hysteresis under neural networks (NNs) estimation framework. In contrast to most existing results of nonlinear systems with time‐delay, the time‐varying delay we consider depends entirely on the number of switching subsystems. Based on the inherent properties of radial basis function NNs, the nonstrict‐feedback structure is effectively compensated. Meanwhile, with the help of the combination of Razumikhin function method, adaptive backstepping scheme, and dynamic surface control approach, the quadratic common Lyapunov function is established for all subsystems, and then an adaptive common control strategy is developed. For arbitrary switching signals, it is shown that all the signals in the closed‐loop system can be remained bounded and the system output can follow a desired signal under the designed controller. Finally, the validity of the presented strategy is verified via two simulation examples.

Stability analysis of Boolean networks with Markov jump disturbances and their application in apoptosis networks

<abstract><p>In this paper, the finite-time stability (FTS) of switched Boolean networks (SBNs) with Markov jump disturbances under the conditions of arbitrary switching signals is studied. By using the tool of the semi-tensor product, the equivalent linear-like form of SBNs with Markov jump disturbances is first established. Next, to facilitate investigation, we convert the addressed system into an augmented Markov jump Boolean network (MJBN), and propose the definition of the switching set reachability of MJBNs. A necessary and sufficient criterion is developed for the FTS of SBNs with Markov jump disturbances under the conditions of arbitrary switching signals. Finally, we give two examples to illustrate the effectiveness of our work.</p></abstract>

Simultaneous and Sequential Control Design for Discrete-Time Switched Linear Systems Using Semi-Definite Programming

The control of switched linear discrete-time systems occurs in multiple engineering fields, where it has been used to deal with complex and non-linear systems. This letter presents two strategies to design control laws for discrete-time switched linear systems, whilst guaranteeing asymptotic stability of the closed loop. Firstly, an arbitrary switching signal is considered. In this scenario a common quadratic Lyapunov function is used for stability, but subsystem Lyapunov functions are employed to improve local subsystem performance. Secondly, a constrained switching signal, associated with subsystem lower dwell time bounds is studied. In this case, a decrease in Lyapunov cost is achieved by design, based on dwell time constraints only, thus removing the need for both a common quadratic Lyapunov function or direct stable switches. It is shown in both cases that the control design problems can be formulated as one or a sequence of semi-definite programming problems, and therefore can be solved efficiently. Finally, two examples are provided in order to illustrate the different techniques presented.

Finite time adaptive fault‐tolerant controller based on neural networks for switched stochastic nonlinear systems with actuator failures and disturbance

SummaryThis article investigates the novel finite time adaptive neural fault‐tolerant controller (FTC) for strict‐feedback switched stochastic systems under arbitrary switching signals and takes into actuator failures including loss of effectiveness faults and bias faults consideration concurrently. Neural networks are utilized to approximate the unknown external disturbance and internal dynamics. On the basis of Itô differential equation and backstepping technique, an adaptive neural finite time FTC method is put forward. It is attested that the closed‐loop systems are semiglobal practical finite time stable in probability and the tracking effects are great. Finally, to further demonstrate the high efficiency of proposed control method, two simulation examples are given.

Dissipativity-Based Two-Dimensional Control and Filtering for a Class of Switched Systems

This paper deals with the dissipative control and filtering problems for the discrete-time two-dimensional (2-D) switched Fornasini-Marchesini (FM) systems. First, the definition of 2-D TSR- ϑ-dissipativity for the FM systems is introduced. By employing the switched quadratic Lyapunov function technique and establishing multiple recursive formulas, sufficient conditions are developed to guarantee that the considered system is asymptotically stable under the arbitrary switching signal (ASS) case and exponentially stable under the restricted switching signal (RSS) case with the 2-D TSR- ϑ-dissipativity, respectively. The special cases, such as the 2-D passivity performance and the 2-D H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance, are also discussed. Based on the obtained dissipative stability conditions, the 2-D TSR- ϑ-dissipative state feedback controller and filter design problems are further studied for the addressed system. Particularly, the extended average dwell time (define this later on in text) technique is utilized for the system under the RSS case. Finally, the effectiveness of the proposed design method is illustrated by numerical examples.

Pinning bipartite synchronization for coupled reaction–diffusion neural networks with antagonistic interactions and switching topologies

In this paper, the bipartite synchronization issue for a class of coupled reaction–diffusion networks with antagonistic interactions and switching topologies is investigated. First of all, by virtue of Lyapunov functional method and pinning control technique, we obtain some sufficient conditions which can guarantee that networks with signed graph topologies realize bipartite synchronization under any initial conditions and arbitrary switching signals. Secondly, for the general switching signal and periodic switching signal, a pinning controller that can ensure bipartite synchronization of reaction–diffusions networks is designed based on the obtained conditions. Meanwhile, a directed relationship between coupling strength and control gains is presented. Thirdly, numerical simulation is provided to demonstrate the correctness and validity of the derived theoretical results for reaction–diffusion systems. We briefly conclude our findings and future work.

Twofold Sliding Controller Design for Uncertain Switched Nonlinear Systems

This paper deals with the problem of controller design for normal nonlinear switched systems with unknown dynamics. The situation assumes that the nonlinear component of the system dynamics is unknown and there are extra uncertain terms and external perturbations affecting the system responses. Unlike previous methods that usually apply artificial neural networks to obtain an approximate model for an unknown dynamics, we use simple adaptive laws to surmount such fluctuations as well as to circumvent the steady state errors in the approaches provided by neural networks or fuzzy logics. No information on the bounds and parameters of the uncertain parts is needed. We design a twofold sliding mode control methodology to stabilize the whole switched system with arbitrary switching signals. To handle the consequences of the inherent chattering, a smooth integral type control signal is constructed. It is proved that once the system states attain the developed sliding manifold, the system becomes insensitive to both the lumped uncertainties and the dynamics of the switched system. The common assumption of a known Lyapunov functions for the subsystems is relaxed and the derived adaptive approach provides nonconservative circumstances for guaranteeing the global stability of the equilibrium state. The theoretical results of this paper are generalized for the canonical nonlinear systems with mismatched uncertainties and a novel adaptive sliding manifold is proposed to suppress the effects of the system mismatching uncertain parts. A comparative computer simulation is developed to examine the effective performance of the introduced controllers.

Channel Coding and Receiver Design for Simultaneous Wireline Information and Power Transfer

For the first time, the recently proposed “talkative power” paradigm combining power electronics and communication engineering is extended by channel coding and advanced receiver design aspects. In this concept, the pulses that control the duty cycle of switched-mode power converters are simultaneously used for data transmission by modifying the pulse phase, pulse frequency, pulse position or pulse width. The data sequence is embedded into the switching signal, similar to random modulation. The data can be used for example in point-to-point links, inside multi-port power converters, and for communication in networked power grids. As an application example a buck converter is studied. Its output voltage is numerically calculated for arbitrary two-level switching signals. The corresponding system model serves as a common framework for switching waveform design, receiver design, and performance analysis. The data sequence is represented by a small deterministic output voltage ripple. Various techniques to improve the data rate and the robustness of the communication are introduced, including line coding, a derivation of the optimum receiver in the sense of maximum-likelihood detection, and forward error correction coding as an option. Although emphasis is on a buck converter, the concept is applicable to other power converter topologies as well.

Regional stability analysis of impulsive switched nonlinear systems with multiple equilibrium points

AbstractThis paper addresses the regional stability problem for impulsive switched nonlinear systems (ISNSs) whose subsystems have more than one equilibrium point, that is, multiple equilibrium points (MEPs) coexist. Meanwhile, we derive analytical results and sufficient conditions about the regional stability. Through investigating the dynamical behavior of ISNSs with MEPs, the multiple Lyapunov functions (MLFs) method is established for the regional stability. It is shown that main results obtained in this paper not only guarantee the regional stability of ISNSs with MEPs under arbitrary switching signals but also provide a new method to determine the corresponding stable regions for the regional stability. Numerical simulations are given to illustrate and verify advantages of our proposed results.

Delayed state feedback predictive control of uncertain nonlinear discrete‐time switched systems with input constraint and state delays

This study addresses the robust predictive control of a class of discrete-time switched systems under arbitrary switching signals. The subsystems of the considered switched system involve polytopic uncertainties, the state delay, non-linear terms, and input constraint. The main goal is to provide two switched delayed state feedback controllers for the cases of known and unknown state delays based on a constrained robust model predictive control method. An appropriate Lyapunov–Krasovskii functional is used to design the controller via an optimisation problem developed as linear matrix inequalities (LMIs). Both approaches are delay dependent because the online LMIs depend on the value of state delay in the first case and the upper bound of the state delay in the second one. The other advantages of the proposed method are considering a non-constrained switching signal, its ability to handle constraints, and shaping a transient response. Finally, numerical examples are provided to illustrate the effectiveness of the theoretical results and also to compare the results with previous researches.

Asymptotic stability and stabilization of discrete‐time switched systems with time‐varying delay

SummaryThis article deals with the problems of stability and stabilization for a class of discrete‐time switched systems with time‐varying delay under arbitrary switching signal. First, sufficient conditions guaranteeing the asymptotic stability of the unforced system are developed, by using the switched Lyapunov‐Krasovskii functional method. Then, based on the obtained results, a state feedback controller is designed in order to ensure the asymptotic stability of the closed‐loop system. Furthermore, slack variables are introduced for more relaxation. The proposed approach is proved to have some less conservative results than some existing works. Finally, numerical examples are provided to illustrate the effectiveness and the merit of the proposed method and to compare the obtained results with some previous works in the literature.

Stability Analysis of Discrete-Time Switched Systems With Unstable Modes: An Improved Ratio-Based Tradeoff Approach

This brief investigates the stability of switched systems with unstable modes in discrete-time context. To enlarge the room for switching scheme design, a new multiple discontinuous Lyapunov functions (MDLFs) method is developed, and a novel mode-dependent average dwell time (MDADT) tradeoff strategy is explored. Subsequently, based on the new MDLFs method, stability criteria are achieved for the systems under arbitrary switching signals with the MDADT-based tradeoff switching scheme. Finally, the proposed results are applied to a Pulse-Width-Modulation driven boost converter to demonstrate the effectiveness.

Sensor fault detection for switched systems using interval observer with L∞ performance

This paper deals with sensor fault detection (FD) for discrete-time switched systems subject to bounded disturbances. A novel approach is investigated to construct residual framers using interval observer with L∞ performance. The proposed technique is used to provide more degrees of design freedom and to obtain accurate FD results. The design conditions of the FD observer are given in terms of Linear Matrix Inequalities (LMIs) adopting firstly a common quadratic Lyapunov function, under an arbitrary switching signal and secondly multiple quadratic Lyapunov functions, under an Average Dwell Time (ADT) switching signal. Furthermore, the FD decision is based on residual intervals generated by the proposed interval observer. The effectiveness of the proposed approach is highlighted through simulation results of an academic example.

Observability of switched Boolean control networks using algebraic forms

<p style='text-indent:20px;'>This paper addresses the observability of a switched Boolean control network (SBCN) using semi-tensor product (STP) of matrices. First, the observability of the SBCN is determined under desirable switching signals and arbitrary switching signals by encoding the switching signal as a boolean input. Then an algorithm is designed for determining the observability. Furthermore, feedback control laws are obtained to guarantee the observability of SBCNs. Examples and corresponding state trajectory graphs are given to illustrate the effectiveness of the given results.

Fault-tolerant anti-synchronization control for chaotic switched neural networks with time delay and reaction diffusion

<p style='text-indent:20px;'>This paper is concerned with the issue of fault-tolerant anti-synchro-nization control for chaotic switched neural networks with time delay and reaction-diffusion terms under the drive-response scheme, where the response system is assumed to be disturbed by stochastic noise. Both arbitrary switching signal and average dwell-time limited switching signal are taken into account. With the aid of the Lyapunov-Krasovskii functional approach and combining with the generalized Itô formula, sufficient conditions on the mean-square exponential stability for the anti-synchronization error system are presented. Then, by utilizing some decoupling methods, constructive design strategies on the desired fault-tolerant anti-synchronization controller are proposed. Finally, an example is given to demonstrate the effectiveness of our design strategies.

Reachability Analysis of Networked Finite State Machine With Communication Losses: A Switched Perspective

Networked finite state machine takes into account communication losses in industrial communication interfaces due to the limited bandwidth. The reachability analysis of networked finite state machine is a fundamental and important research topic in blocking detection, safety analysis, communication system design and so on. This paper is concerned with the impact of arbitrary communication losses on the reachability of networked finite state machine from a switched perspective. First, to model the dynamics under arbitrary communication losses in communication interfaces (from the controller to the actuator), by resorting to the semi-tensor product (STP) of matrices, a switched algebraic model of networked finite state machine with arbitrary communication losses is proposed, and the reachability analysis can be investigated by using the constructed model under arbitrary switching signal. Subsequently, based on the algebraic expression and its transition matrix, necessary and sufficient conditions for the reachability are derived for networked finite state machine. Finally, some typical numerical examples are exploited to demonstrate the effectiveness of the proposed approach. Note that current results provide valuable clues to design reliable and convergent Internet-of-Things networks.

Feedback stabilization control design for switched Boolean control networks

In this paper, the design of all possible switching signal-dependent state feedback and output feedback stabilizers for switched Boolean control networks (SBCNs) under arbitrary switching signal is investigated. By making use of the algebraic state-space approach to SBCNs, necessary and sufficient conditions for the stabilization at a given equilibrium point are presented. A new algorithm is proposed to determine all possible complete families of controllable sets for SBCNs, thereby all possible switching signal-dependent state feedback and output feedback controllers are obtained. Furthermore, we derive necessary and sufficient conditions for the solvability of the output regulation problem, and we show that, upon satisfying such conditions, also this problem can be solved by means of switching signal-dependent state feedback and output feedback controllers. At last, the proposed results are supported by examples.