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This paper adopts a quantization-dependent Lyapunov function to study the output feedback stabilization problem of a switched system subject to output event-triggered sampling and quantization. First, a new event-triggered mechanism related to quantization parameters is proposed, which can obtain a trade-off between the event-triggered frequency and quantization density on the premise of ensuring asymptotic stability of the switched system. Moreover, sufficient conditions are obtained to ensure asymptotic stability of the switched system by a quantization-dependent Lyapunov function. Lastly, through a numerical simulation and PWM-driven boost converter system, we demonstrate the availability of the proposed quantization-dependent Lyapunov function and event-triggered mechanism methods based on quantization parameters, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we propose new algebraic Gramians for continuous-time switched linear systems, which satisfy generalized Lyapunov equations. The main contribution of this paper is twofold. First, we show that the ranges of those Gramians encode the reachability and observability spaces of a switched linear system. As a consequence, a simple Gramian-based criterion for reachability and observability is established. Second, a balancing-based model order reduction technique is proposed and, under some sufficient conditions, stability preservation and an error bound are shown. Finally, the efficiency of the proposed method is illustrated by means of numerical examples. [ABSTRACT FROM AUTHOR]

This paper is concerned with the distributed $H_\infty $ filtering problem of discrete-time switched linear systems in sensor networks in face of packet dropouts and quantization. Specifically, due to the packet dropout phenomenon, the filters may lose access to the real-time switching signal of the plant. It is assumed that the maximal packet dropout number of switching signal is bounded. Then, a distributed filtering system is proposed by further considering the quantization effect. Based on the Lyapunov stability theory, a sufficient condition is obtained for the convergence of filtering error dynamics. The filter gain design is transformed into a convex optimization problem. In this paper, a quantitative relation between the switching rule missing rate and filtering performance is established. Furthermore, the upper bound of the switching rule missing rate is also calculated. Finally, the effectiveness of the proposed filter design is validated by a simulation study on the pulse-width-modulation-driven boost converter circuit. The impact of noise covariance, system dynamics, and network connectivity is studied, and some discussions are presented on how these parameters affect the filtering performance. [ABSTRACT FROM PUBLISHER]

This paper addresses the problems of determining the \mathcal H_2 norm and the root mean square (RMS) gain of continuous-time switched linear systems. A novel class of Lyapunov functions is proposed for reaching this goal, called homogeneous rational Lyapunov functions (HRLFs). It is shown that sufficient conditions for establishing upper bounds of the sought performance indexes in the case of arbitrary switching can be given in terms of linear matrix inequality (LMI) feasibility tests by searching for an HRLF of chosen degree. Moreover, it is shown that these conditions are also necessary by searching for an HRLF of degree sufficiently large. It is worth mentioning that necessary and sufficient LMI conditions have not been proposed yet in the literature for the considered problems. Hence, the paper continues by considering the case of switching with dwell time constraints, showing that analogous LMI conditions can be obtained for this case by searching for a family of HRLFs mutually constrained by the dwell time specification. Some numerical examples illustrate the proposed methodology and highlight the advantages with respect to the existing works. [ABSTRACT FROM AUTHOR]

This paper addresses the event-triggered dynamic output feedback control for switched linear systems with frequent asynchronism. Different from existing work, which limits at most once switching during an interevent interval, we adopt the average dwell time approach without limiting the minimum dwell time of each subsystem, and thus frequent switching is allowed to happen in an interevent interval. Since the difficulty in acquiring the full information of system states, the dynamic output feedback controller is taken into account to stabilize the switched system. By employing a controller-mode-dependent Lyapunov functional, stability criterion is proposed for the resulting closed-loop system, based on which the dynamic output feedback controller together with the mode-dependent event-triggered mechanism is codesigned. Besides, the existence of the lower bound on interevent intervals is attentively discussed, which gets rid of the Zeno behavior. Finally, the effectiveness of the proposed method is illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper deals with the dead-beat stabilizability of autonomous discrete-time switched linear systems. Based on a constructive necessary and sufficient condition for dead-beat stabilizability, we propose two algorithms. The first one is concerned with the problem of testing dead-beat stabilizability and computing the shorter stabilizing mode sequence, whenever it exists. The other one implements a method to construct a switched system whose shorter dead-beat stabilizing sequence has a prescribed length. Then, we present numerical assessments and possible applications. [ABSTRACT FROM AUTHOR]

In this paper, we consider the l\infty gain characterizations of linear switched systems (LSS) and present various relevant results on their exact computation and optimization. Depending on the role of the switching sequence, we study two broad cases: first, when the switching sequence attempts to maximize, and second, when it attempts to minimize the l\infty gain. The first, named as worst-case throughout the paper, can be related to robustness of the system to uncontrolled switching; the second relates to situations when the switching can be part to the overall decision making. Although, in general, the exact computation of l\infty gains is difficult, we provide specific classes, the input-output switching systems, for which it is shown that linear programming can be used to obtain the worst-case l\infty gain. This is a sufficiently rich class of systems as any stable LSS can be approximated by one. Certain applications to robust control design are provided where we show that a switched compensation independently of the plant has no advantage over a linear time invariant (LTI) compensation, and further, if the plant is strictly causal, even a switched compensation which has a matched switching with the plant does not provide a better performance over an LTI compensation. Also, we present a new necessary and sufficient condition to check the stability of LSS in form of a model matching problem. On the other hand, if one is interested in minimizing the l\infty gain over the switching sequences, we show that, for finite impulse response (FIR) switching systems the minimizing switching sequence can be chosen to be periodic. For input-only or output-only switching an exact, readily computable, characterization of the minimal l\infty gain is provided, and it is shown that the minimizing switching sequence is constant, which, as also shown, is not true for input-output switching. [ABSTRACT FROM AUTHOR]

This paper investigates standard $H_\infty$ control of switched systems via dwell-time switchings without posing any internal stability requirements on subsystems of the switched systems. First, a sufficient condition is formed by specifying lower and upper bounds of the dwell time, constraining upper bound of derivative of a Lyapunov function of the active subsystem, and forcing the Lyapunov function values of the overall switched system to decrease at switching times to achieve standard $H_\infty$ control of unforced switched linear systems. Then, in the same framework of the dwell time, sufficient conditions are given for that of the corresponding forced switched linear systems by further designing state feedback controllers. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

Controlled distinguishability of two dynamical systems is the property of the systems that guarantees the existence of a control input generating different outputs of the systems regardless of their initial state vectors. These inputs are referred in the literature as discerning control inputs. In this paper, a necessary and sufficient condition for controlled distinguishability of continuous-time bilinear systems is established. It generalizes the classic one provided in the literature for the class of linear systems and a method for designing discerning inputs of bilinear systems that stabilize the systems is also proposed. [ABSTRACT FROM AUTHOR]

This paper considers the optimal control problem of linear switched systems with linear quadratic (LQ) cost or multiple LQ cost. By adopting an embedding transformation, the switching design problem is relaxed and transformed into a traditional optimal control problem. The bang–bang-type solutions of the embedded optimal control problems are obtained for both the positive definite LQ cost case and the multiple LQ cost case, which are the optimal solutions to the original problems. The switching sequence of modes and the switching instants can be calculated by solving a closed-form optimal switching condition. The optimal state feedback control law is determined simultaneously. Finally, numerical results are provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we consider the event-triggered control problem for continuous-time switched linear systems. It is assumed that only the sampled information of system state and switching signal is available to the controller at each sampling instant. Based on a mode-dependent event-triggered transmission scheme, the closed-loop system is modeled as a switched system with delayed state and augmented switching signal. Then, an exponential stability condition, characterized by the dwell time and average dwell time of the switching signal, is obtained. The condition presents an extension of the multiple Lyapunov functional method based stability analysis for sampled-data control of nonswitched system. Consequently, the design methods for state-feedback controller gains and event-triggered parameters are then formulated by the properly selected quadratic Lyapunov functional. The analysis results are significant and also lead to an important step to study the event-triggered control for switched system. Finally, based on the definition of event-trigger efficiency, the effectiveness and improvement of the proposed approach are illustrated by two numerical examples. [ABSTRACT FROM AUTHOR]

This paper considers a singular problem in optimal control of continuous-time bimodal switched linear systems. A relaxed switched system with a continuous-valued switching signal is considered and the representations of singular control and singular arcs are derived. The similarity in the structure between the singular control and a stabilizing switching law is revealed and an approximation of the singular control by a well-defined switching signal is addressed. The results are demonstrated by numerical simulations. [ABSTRACT FROM AUTHOR]

This note points out certain limitations of our results from the paper mentioned in the title, and provides a modified approach to overcome these limitations. Specifically, the observer design addressed in the aforementioned paper is, in general, only applicable to switched linear systems with invertible state reset maps and this note presents a modified algorithm for state estimation that can also handle non-invertible state reset maps. In the process, we also identify some equalities from that paper which may not hold in general for arbitrary state reset maps. [ABSTRACT FROM PUBLISHER]

This paper addresses the aggregation issues of competitive multiagent systems (CMASs) consisting of competitive agents with multimodes and saddle points. In such CMASs, due to existing mutual competitions, every agent is equipped with finite multimodes, and every mode in any agent is described as a second-order linear time-invariant (LTI) control system. When the origin is the same saddle point of all modes of agents, to investigate aggregation of the CMASs with switching strategies, we first use switched LTI systems with saddle points to formulate such CMASs. Then, two new stability concepts, called initial-state-dependent (ISD) stability and initial-state-independent (ISI) stability, are defined for the CMASs. Based on these new stability concepts, a practical criterion of local/global ISI asymptotic aggregation is proposed for the CMASs. A local/global ISD/ISI asymptotical-stabilizing-control observed as distributed controls of multimodes, stabilizing-switching-paths, and a corresponding algorithm are all designed for local/global aggregation of such CMASs with switching delays. Finally, a numerical example illustrates the effectiveness and practicality of our new results. [ABSTRACT FROM AUTHOR]

This paper addresses the output reachable set estimation problem for continuous-time switched linear systems consisting of Hurwtiz stable subsystems. Based on a common Lyapunov function approach, the output reachable set is estimated by a union of bounding ellipsoids. Then, multiple Lyapunov functions with time-scheduled structure are employed to estimate the output reachable set for switched systems under dwell-time constraint. Furthermore, the safety verification problem of uncertain switched systems is investigated based on the result of output reachable set estimation. First, a sufficient condition ensuring the existence of an approximate bisimulation relation between two switched linear systems with a prescribed precision is proposed. Then, the safety verification for an uncertain switched system can be performed through an alternative safety verification for a switched system with exact parameters. Numerical examples are provided to illustrate our results. [ABSTRACT FROM AUTHOR]

This paper introduces the notion of common zeroing-output systems (CZOS) to analyze the stability of switched systems. The concept of CZOS allows one to verify weak zero-state detectability. It characterizes a common behavior of any individual subsystem when the output signal for each subsystem is “approaching” zero. Heuristically speaking, it removes the effect of switching behavior, and thus enables one to analyze stability properties in systems with complex switching signals. With the help of CZOS, the Krasovskii–LaSalle theorem can be extended to switched nonlinear time-varying systems with both arbitrary switching and more general restricted switching cases. For switched nonlinear time-invariant systems, the needed detectability condition is further simplified, leading to several new stability results. Particularly, when a switched linear time-invariant system is considered, it is possible to generate a recursive method, which combines a Krasovskii–LaSalle result and a nested Matrosov result, to find a CZOS if it exists. The power of the proposed CZOS is demonstrated by consensus problems in literature to obtain a stronger convergence result with weaker conditions. [ABSTRACT FROM AUTHOR]

This paper investigates the state observer design of a class of unknown input switched linear systems via mode-dependent dwell time switchings. The distinguishing feature of the proposed method is that strong detectability condition of subsystems of the switched systems is unnecessarily required. First, a time-varying coordinate transformation is introduced to design a suitable reduced-order observer for each subsystem. Then, computable sufficient conditions on the synthesis of the observers are proposed in the framework of a mode-dependent dwell time technique. Since the observer of an individual subsystem cannot be designed due to unavailability of strong detectability condition of the subsystem, the state of the switched system is estimated under the condition of confining the dwell time by a pair of upper and lower bounds, restricting the growth of the Lyapunov function of the active subsystem and forcing “energy” of the overall switched system to decrease at switching instants. Finally, an example is presented to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we study the stability of networked control systems (NCSs) that are subject to time-varying transmission intervals, time-varying transmission delays, and communication constraints. Communication constraints impose that, per transmission, only one node can access the network and send its information. The order in which nodes send their information is orchestrated by a network protocol, such as, the Round-Robin (RR) and the Try-Once-Discard (TOD) protocol. In this paper, we generalize the mentioned protocols to novel classes of so-called “periodic” and “quadratic” protocols. By focusing on linear plants and controllers, we present a modeling framework for NCSs based on discrete-time switched linear uncertain systems. This framework allows the controller to be given in discrete time as well as in continuous time. To analyze stability of such systems for a range of possible transmission intervals and delays, with a possible nonzero lower bound, we propose a new procedure to obtain a convex overapproximation in the form of a polytopic system with norm-bounded additive uncertainty. We show that this approximation can be made arbitrarily tight in an appropriate sense. Based on this overapproximation, we derive stability results in terms of linear matrix inequalities (LMIs). We illustrate our stability analysis on the benchmark example of a batch reactor and show how this leads to tradeoffs between different protocols, allowable ranges of transmission intervals and delays. In addition, we show that the exploitation of the linearity of the system and controller leads to a significant reduction in conservatism with respect to existing approaches in the literature. [ABSTRACT FROM AUTHOR]

Switched dynamical systems can be found in many practical electronic circuits, such as various kinds of power converters, chaos generators, etc. This paper is concerned with the filter design problem for a class of switched system with average dwell time switching. Mode-dependent full-order filters are designed taking a more practical phenomenon, the asynchronous switching into account, where “asynchronous” means that the switching of the filters to be designed has a lag to the switching of the system modes. New results on the stability and l2-gain analyses for the systems are first given where the Lyapunov-like functions during the running time of subsystems are allowed to increase. In light of the proposed Lyapunov-like functions, the desired mode-dependent filters can be designed in that the unmatched filters are allowed to perform in the interval of the asynchronous switching before the matched ones are applied. In H\infty sense, the problem of asynchronous filtering for the underlying systems in linear cases is formulated and the conditions of the existence of admissible asynchronous filters are obtained. Two examples are provided to show the potential of the developed results. [ABSTRACT FROM PUBLISHER]

In this paper we deal with the stabilizability property for discrete-time switched linear systems. A recent necessary and sufficient characterization of stabilizability, based on set theory, is considered as the reference for comparing the computation-oriented sufficient conditions. The classical BMI conditions based on Lyapunov-Metzler inequalities are considered and extended. Novel LMI conditions for stabilizability, derived from the geometric ones, are presented that permit to combine generality with computational affordability. For the different conditions, the geometrical interpretations are provided and the induced stabilizing switching laws are given. The relations and the implications between the stabilizability conditions are analyzed to infer and compare their conservatism and their complexity. [ABSTRACT FROM AUTHOR]

This paper introduces the concept of consistency for continuous-time switched linear systems having the switching function as a primary control signal to be designed. A switching control strategy is strictly consistent whenever it improves performance compared to the ones of all isolated subsystems. Conditions under which a min-type switching strategy is strictly consistent for the classes of \cal H2 and \cal H\infty performance indexes are determined. This property makes clear the importance of switching systems control design in both theoretical and practical application frameworks. Moreover, with this property it is not necessary to assume that all the subsystems are not stable in order to make a switching strategy design problem well posed. The theory is illustrated by means of several academic examples. [ABSTRACT FROM PUBLISHER]

This paper presents a characterization of observability and an observer design method for switched linear systems with state jumps. A necessary and sufficient condition is presented for observability, globally in time, when the system evolves under predetermined mode transitions. Because this characterization depends upon the switching signal under consideration, the existence of singular switching signals is studied alongside developing a sufficient condition that guarantees uniform observability with respect to switching times. Furthermore, while taking state jumps into account, a relatively weaker characterization is given for determinability, the property that concerns with recovery of the original state at some time rather than at all times. Assuming determinability of the system, a hybrid observer is designed for the most general case to estimate the state of the system and it is shown that the estimation error decays exponentially. Since the individual modes of the switched system may not be observable, the proposed strategy for designing the observer is based upon a novel idea of accumulating the information from individual subsystems. Contrary to the usual approach, dwell-time between switchings is not necessary, but the proposed design does require persistent switching. For practical purposes, the calculations also take into account the time consumed in performing computations. [ABSTRACT FROM AUTHOR]

This paper is concerned with the derivation of a model reference adaptive control (MRAC) scheme for multimodal piecewise-affine (PWA) and piecewise-linear systems. The control allows the plant to track asymptotically the states of a multimodal piecewise affine (or smooth) reference model. The reference model can be characterized by a number and geometry of phase space regions that can be entirely different from those of the plant. Numerical simulations on a set of representative examples confirm the theoretical derivation and proof of stability. [ABSTRACT FROM AUTHOR]

In this paper, the stability and stabilization problems for a class of switched linear systems with mode-dependent average dwell time (MDADT) are investigated in both continuous-time and discrete-time contexts. The proposed switching law is more applicable in practice than the average dwell time (ADT) switching in which each mode in the underlying system has its own ADT. The stability criteria for switched systems with MDADT in nonlinear setting are firstly derived, by which the conditions for stability and stabilization for linear systems are also presented. A numerical example is given to show the validity and potential of the developed techniques. [ABSTRACT FROM PUBLISHER]

This paper studies the quadratic regulation problem for discrete-time switched linear systems (DSLQR problem) on an infinite time horizon. A general relaxation framework is developed to simplify the computation of the value iterations. Based on this framework, an efficient algorithm is developed to solve the infinite-horizon DSLQR problem with guaranteed closed-loop stability and suboptimal performance. Due to these guarantees, the proposed algorithm can be used as a general controller synthesis tool for switched linear systems. [ABSTRACT FROM PUBLISHER]

In this paper, we first establish a stability result for a class of linear switched systems involving Kronecker product. The problem is interesting in that the system matrix does not have to be Hurwitz at any time instant. This class of linear switched systems arises in the control of multi-agent systems under switching network topology. As applications of this stability result, we give the solvability conditions for both the leaderless consensus problem and the leader-following consensus problem for general marginally stable linear multi-agent systems under switching network topology. In contrast with some existing results, our results only assume that the dynamic graph is uniformly connected. [ABSTRACT FROM AUTHOR]

In this paper we consider the class of discrete-time switched systems switching between p autonomous positive subsystems. First, sufficient conditions for testing stability, based on the existence of special classes of common Lyapunov functions, are investigated, and these conditions are mutually related, thus proving that if a linear copositive common Lyapunov function can be found, then a quadratic positive definite common function can be found, too, and this latter, in turn, ensures the existence of a quadratic copositive common function. Secondly, stabilizability is introduced and characterized. It is shown that if these systems are stabilizable, they can be stabilized by means of a periodic switching sequence, which asymptotically drives to zero every positive initial state. Conditions for the existence of state-dependent stabilizing switching laws, based on the values of a copositive (linear/quadratic) Lyapunov function, are investigated and mutually related, too. [ABSTRACT FROM PUBLISHER]

This paper investigates sufficient conditions for the convergence to zero of the trajectories of linear switched systems. We provide a collection of results that use weak dwell-time, dwell-time, strong dwell-time, permanent and persistent activation hypothesis. The obtained results are shown to be tight by counterexample. Finally, we apply our result to the three-cell converter. [ABSTRACT FROM AUTHOR]