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This study focuses on bumpless transfer (BT) fault detection in switched linear systems operating under mode‐dependent average dwell time (MDADT) switching. We propose a piecewise fault detection filter (FDF) inspired by the segmentation concept inherent in the multiple discontinuous Lyapunov function (MDLF) approach. This filter generates a residual signal that effectively minimizes the amplitude of residual bumps, surpassing the performance of traditional non‐piecewise FDFs. We introduce a new definition of residual BT performance, aimed at reducing residual bump amplitude during filter transitions. The goal is to design the piecewise FDF such that the augmented system maintains asymptotic stability with weighted H∞$$ {H}_{\infty } $$ performance, while also meeting the residual BT performance criteria. The feasibility of achieving H∞$$ {H}_{\infty } $$ BT fault detection filtering is established through linear matrix inequalities (LMIs), leveraging the MDLF and MDADT strategies. The efficacy and benefits of the proposed BT piecewise FDF design are demonstrated through simulations on a boost converter. [ABSTRACT FROM AUTHOR]

This article studies the stability problem of discrete‐time positive switched linear systems by introducing a nonzero elements chain method. Compared to existing works, the highlight of this article is reflected in the inclusiveness of the subsystem, that is, each subsystem is allowed to be stable, marginally stable or even unstable. Some sufficient conditions depending on the characteristics of system matrices and the time‐dependent switching signals are established, so as to guarantee the exponential stability of positive switched linear systems. In addition, the main result is extended to the case of time‐varying delay. At last, the superiority of the obtained results is well verified by numerical examples. [ABSTRACT FROM AUTHOR]

Summary: Ultra‐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. [ABSTRACT FROM AUTHOR]

Switched linear systems are important in providing a convenient method to represent many practical systems. This paper investigates the performance analysis of switched linear systems under arbitrary switching. Computational algorithms based on square coordinate transformations are presented to obtain the least μ1 measure. Theoretical results showed that sequences of the least μ1 matrix set measure obtained by two different algorithms are convergent and the limit gives an upper bound estimation of the spectral abscissa. A numerical example is presented to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The purpose of this article is to survey some sparsity‐inducing methods in system identification and state estimation. Such methods can be divided into two main categories: methods inducing sparsity in the parameters and those sparsifying the prediction error. In the last class we discuss in particular the least absolute deviation estimator and its robustness properties with respect to sparse noise in both cases of univariate and multivariate measurements. We also discuss the application of sparsity‐inducing methods to switched system identification and to state estimation for linear systems in the presence sparse and dense measurement noises. While the presentation focuses essentially on bridging some existing results, some technical refinements, and new features are also provided. [ABSTRACT FROM AUTHOR]

The sampled‐data event‐triggered control problem of switched linear systems in which both the sampled information of the system states and the switching signal are available to the controller at the event‐triggered transmission instants is studied here. The coexistence of the event‐triggered transmission and the switching behaviour makes the switching signal of the controller and the switching signal of the system asynchronous. By constructing a new multiple Lyapunov–Krasovskii functional and using the asynchronous switching method, the exponential stability conditions characterised by mode‐dependent average dwell time of the switching signal are proposed. Then, the corresponding solvability conditions for the event‐triggered state feedback controller are formulated. Finally, a numerical example is given to illustrate the validity of the proposed results. [ABSTRACT FROM AUTHOR]

In this study, the stability problem of continuous‐time switched systems composed fully of unstable subsystems is considered. Unlike the hybrid conditions derived in previous literature, this study used a novel time‐dependent quadratic Lyapunov function approach and a convex sufficient condition for switched linear systems is proposed in the framework of bounded maximum average dwell time (BMADT). The resulting condition in this study is enforced using the sum of squares programming. Then, the condition for switched linear systems is extended to uncertain systems and the robust stability condition is derived. Moreover, a new stability result of continuous‐time switched systems with all subsystems unstable is investigated based on the BMADT conditions. The simulation shows that it is better than the results in previous literature. Two numerical examples are proposed to illustrate the authors' approach. [ABSTRACT FROM AUTHOR]

Summary: In this paper, several equivalent stability conditions for switched linear systems with dwell time are presented. Both continuous‐time and discrete‐time cases are considered. For the continuous‐time case, the conditions that are convex in system matrices are presented in terms of infinite‐dimensional linear matrix inequalities (LMIs), which are not numerically testable. Then, by adopting the sum of square (SOS) and piecewise linear approach, computable conditions are formulated in terms of SOS program and LMIs. Compared to the literature, less conservative results can be obtained through solving these conditions for the same polynomial degree or discretized order. For the discrete‐time case, the stability conditions, which are convex in system matrices, are numerically testable. The convexity comes at the price of increment of computational complexity. Furthermore, by adopting the convexification approach, sufficient stability conditions of switched linear systems with polytopic uncertainties are derived, both for continuous‐time and discrete‐time cases. At last, several examples are given to demonstrate the correctness and advantages of our results. [ABSTRACT FROM AUTHOR]

In this study, the authors study the issue of H∞ control of continuous switched systems based on the input and output strict passivity. First of all, for switched non‐linear systems, by constructing non‐linear controllers and an appropriate switching rule, a sufficient condition is given to guarantee the existence of a solution to the H∞ control problem based on the multiple Lyapunov functions method. It only requires that each subsystem exhibits input and output strict passivity in the activation interval, and not in the whole time domain. Next, for switched linear systems, a sufficient condition is obtained to guarantee the existence of a solution to the H∞ control problem based on the linear matrix inequality, and the controllers with explicit expressions of subsystems are designed. Finally, two examples are given to verify the feasibility and effectiveness of the results. [ABSTRACT FROM AUTHOR]

This study proposes a systematic control design approach to consider jointly the event‐triggered communication mechanism and state‐feedback control for switched linear systems. The systems determine the necessary samplings of the feedback signal by constructing predefined events that can reduce redundant signal transmission and updates. Specifically, the first main step in the design is to construct sufficient conditions for stability analysis in the form of linear matrix inequalities to utilise fully the idea of average dwell time. With the proposed event‐triggering mechanism, the design renders the resulting switched closed‐loop system finite‐time bounded. Subsequently, the authors present the conditions for finding the parameter of the event‐triggered sampling mechanism and the state‐feedback sub‐controller gains. Then, the results for the full state feedback control case are further extended to systems incorporating observer‐based state‐feedback control motivated by practical applications. For each case, an estimate of the positive lower bound on the inter‐execution times is further derived to avoid Zeno behaviour. A numerical example is presented to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

For systems with switched linear dynamics and affected by persistent switched exosignals, we propose a new hybrid control approach to achieve not only closed-loop stability but also tracking and/or rejection of persistent references/disturbances generated by multiple exosystems, namely, output regulation. It is assumed that both controlled plant and exosystem are described by switched linear models. The proposed hybrid controller/output regulator is specified as a switching impulsive system, where the controller states will undergo impulsive jumps at each switching instant. Based on the average dwell time switching technique, it has been shown how to completely reduce the synthesis problem of the hybrid controller to a set of linear matrix equations and linear matrix inequalities. Both continuous-time and discrete-time cases are discussed. To demonstrate its usefulness, the proposed hybrid control method has been applied to solve the output regulation problem for a mechanical system. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This study investigates the problem of finite‐time stabilisation for a class of switched linear systems with interval time‐varying delay and parametric uncertainties. First, sufficient conditions for the finite‐time stability of unforced switched systems are presented based on the average dwell time method and on the appropriate multiple Lyapunov‐like functions that contain information regarding the lower and upper bounds of delay. A state feedback controller is then proposed for uncertain switched systems, with interval time‐varying delay, which guarantees finite‐time stabilisation of closed‐loop systems. These conditions are formulated using a set of linear matrix inequalities and are dependent on the size of the time delay. Moreover, the criteria obtained are less conservative than some existing results because of the assumption of the upper bound of the derivative of the Lyapunov‐like functions, without the neglect of any useful terms. Finally, two examples are provided to demonstrate the effectiveness of the proposed method. The first is a numerical example, and the second is a practical example involving river pollution control. [ABSTRACT FROM AUTHOR]

The authors study the stabilisation problem of switched linear systems with sampled and quantised output feedback. They assume that every mode of the plant is stabilisable and observable and that a feedback gain is given for each mode. The controller receives the information about the active mode of the plant only at each sampling instant. Therefore, the controller mode may not synchronise with the plant mode after intersample switching. They construct update rules of quantisation scales to avoid the saturation of the quantiser due to mode mismatches. An encoding and control strategy is designed to guarantee asymptotic stability of the closed‐loop system under slow‐switching assumption described by dwell time and average dwell time. [ABSTRACT FROM AUTHOR]

This study is concerned with the problem of composite anti‐disturbance control for switched linear systems with multiple disturbances. The authors' aim is to construct a disturbance observer to estimate the disturbance generated by an exogenous system, then design a composite controller based on the disturbance observer and a mixed state‐dependent and time‐driven switching law, such that the closed‐loop system is internally stable, and different types of disturbances are attenuated and rejected. First, a mixed switching law is designed, which guarantees a dwell time even when all subsystems are unstable. Then, a sufficient condition ensuring the solvability of the composite anti‐disturbance control problem is presented via multiple Lyapunov functions. Finally, the effectiveness of the proposed control design scheme is illustrated by its application to an aero‐engine, which cannot be handled by the existing approaches. [ABSTRACT FROM AUTHOR]

This study addresses the stability problem of perturbed switched systems with time‐varying delays and uncertainties. The considered switching signals include five classes and the uncertainties take values on compact sets. It is assumed that the nominal system (perturbation‐free system) is robustly uniformly exponentially stable and that the perturbations satisfy vanishing condition plus one of the following three constraints: being locally Lipschitz at origin, globally Lipschitz, and differentiable at origin. By 'vanishing', the authors mean that the perturbation is zero at origin. With these assumptions, it is first revealed that for switched systems being homogeneous of degree one, if the perturbation is sufficiently small, then the perturbed system preserves the stability property of the nominal system, locally or globally, depending on perturbation itself. These results are then applied to switched linear systems with delays, showing that the same conclusion holds for such systems with four types of most frequently encountered uncertainties. Finally, an example is provided to illustrate the proposed theoretical results. [ABSTRACT FROM AUTHOR]

The usability of underdetermined state feedback in the context of pole placement, eigenstructure assignment, stabilization and robustness analysis of continuous and switched linear systems is explored. Analytical tools for system design and analysis are discussed from the geometric perspective. Thereby, several new results are obtained and some well-known ones are recovered and generalized by utilization of the computational methods based on the concept of invariance subspaces. [ABSTRACT FROM AUTHOR]

This study considers the fault detection problem for a class of switched linear systems when the observer matching condition is not satisfied. Without using decoupling transformations, a residual signal, based on reduced order sliding mode observers, is introduced for the detection of faults which occur on the continuous part of the system. Two numerical simulations on the cascade multicellular converter and on the boost converter illustrate the effectiveness of the proposed fault detection scheme. [ABSTRACT FROM AUTHOR]

This study is concerned with the problem of finite‐time boundedness analysis for switched delay systems with the average dwell time. By combining the Jensen inequality and the reciprocally convex approach, a sufficient condition is derived to guarantee the finite‐time boundedness of switched linear systems subject to time‐varying delays. It is shown that the obtained result can achieve better performance comparing with the previous ones. Finally, simulation examples are provided to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

SUMMARY This paper deals with networked control systems design, under the constraint of limited bandwidth on the communication channel. A linear quadratic problem for a fixed sampling period is solved, and this result is used for the development of [ABSTRACT FROM AUTHOR]

Up to now, the potential assumption of most existing results for finite‐time stability and finite‐time boundedness of switched linear systems is that each subsystem should be finite‐time stable or finite‐time bounded. If any one subsystem of switched systems is not finite‐time stable or finite‐time bounded, the previous results may not be true anymore. In this paper, finite‐time stability and finite‐time boundedness of switched linear systems with subsystems that are not finite‐time stable or finite‐time bounded are discussed. Sufficient conditions are given under which switched linear systems with subsystems that are not finite‐time stable or finite‐time bounded is guaranteed to be still finite‐time stable or finite‐time bounded. The results also show the effect of the switching signals on finite‐time stability and finite‐time boundedness of switched linear systems. Moreover, finite‐time L2 ‐gain of switched linear systems with subsystems which are not finite‐time bounded is also given to measure its disturbance tolerance capability in the fixed time interval. A numerical example is employed to verify the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

ABSTRACT In this paper, we study a quadratic stabilizability problem via switched observer for uncertain continuous-time switched linear systems in the sense that the subsystem's matrices are represented as a polytopic linear combination of vertex matrices. Firstly, sufficient conditions for polytopic uncertain continuous-time switched linear systems to be quadratically stabilizable via state feedback are summarized. Next, sufficient conditions for polytopic uncertain switched linear systems to be quadratically stabilizable via switched observer are given under the assumption that output matrices of subsystems have no uncertainties. Further, a numerical example is also investigated. [ABSTRACT FROM AUTHOR]

Finite‐time stability and finite‐time boundedness for a class of switched linear systems with time‐varying delay are studied. Sufficient conditions which guarantee switched linear systems with time‐varying delay finite‐time stable or finite‐time bounded are presented. These conditions are delay‐dependent and are given in terms of linear matrix inequalities. Average dwell time of switching signals is also given such that switched linear systems are finite‐time stable or finite‐time bounded. Moreover, finite‐time weighted L2 ‐gain of switched linear systems with time‐varying delay are also given to measure its disturbance tolerance capability in the fixed time interval. Detail proofs are accomplished by using multiple Lyapunov‐like functions. An example is employed to verify the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]