Vector incremental L2-gain and incremental stability for switched nonlinear systems

This paper studies vector incremental L₂-gain and incremental stability for switched nonlinear systems using individual incremental gains and multiple storage functions. Firstly, a vector incremental L₂-gain concept for switched nonlinear systems is proposed. Each subsystem is not required to have incremental L₂-gain, but it has its own incremental L₂-gain and the related storage function, when it is active. The transformation of “energy” from the active subsystem to each inactive subsystem is characterized by cross-supply rates. Then, we show that a switched nonlinear system who has vector incremental L₂-gain can be incrementally stabilized under some constraints on the energy change of inactive subsystems. Secondly, a state-dependent switching law is designed to achieve vector incremental L₂-gain, even if each subsystem does not have incremental L₂-gain in the classic sense. Thirdly, each switched system is not required to have vector incremental L₂-gain, but the feedback interconnection of switched nonlinear systems is incrementally stabilized by the design of a composite switching law. The switching law allows the two switched systems switch asynchronously. Two examples are provided to verify the effectiveness of the proposed method.     

Stability and L2-gain analysis for switched neutral systems with mixed time-varying delays

This paper considers the stability and L₂-gain for a class of switched neutral systems with time-varying discrete and neutral delays. Some new delay-dependent sufficient conditions for exponential stability and weighted L₂-gain are developed for a class of switching signals with average dwell time. These conditions are formulated in terms of linear matrix inequalities (LMIs) and are derived by employing free weighting matrices method. As a special case of such switching signals, we can obtain exponential stability and normal L₂-gain under arbitrary switching signals. Finally, two numerical examples are given to illustrate the effectiveness of the theoretical results.     

Stability and L2-gain analysis of switched input delay systems with unstable modes under asynchronous switching

We consider the stability and L₂-gain analysis problem for a class of switched linear systems. We study the effects of the presences of input delay and switched delay in the feedback channels of the switched linear systems with an external disturbance. By contrast with the most of the contributions available in literatures, we do not require that all the modes of the switched system are stable when input delay appears in the feedback input. By reaching a compromise among the matched-stable period, the matched-unstable period, and the unmatched period and permitting the increasing of the multiple Lyapunov functionals on all the switching times, the solvable conditions of exponential stability and weighted L₂-gain are developed for the switched system under mode-dependent average dwell time scheme (MDADT). Finally, numerical examples are given to illustrate the effectiveness of the proposed theory.     

Distributed event-triggered sliding mode control of switched systems

This paper investigates the problem of distributed event-triggered sliding mode control (SMC) for switched systems with limited communication capacity. Moreover, the system output and switching signals are both considered to be sampled by distributed digital sensors, which may cause control delay and asynchronous switching. First of all, a novel distributed event-triggering scheme for switched systems is proposed to reduce bandwidth requirements. Then, a state observer is designed to estimate the system state via sampled system output with transmission delay. Based on the observed system state, a switched SMC law and corresponding switching law are designed to guarantee the exponential stability of the closed-loop system with H_∞ performance. Finally, an application example is given to illustrate the effectiveness of the proposed method.     

H∞ output-feedback control for discrete-time switched linear systems via asynchronous switching

In this paper, we consider the H_∞ hybrid dynamical output-feedback control problem for discrete-time switched linear systems under asynchronous switching. A time-varying multiple Lyapunov-like-function (MLF) approach is applied to derive sufficient conditions that guarantee the stability and weighted l₂-gain performance of the closed-loop systems, where the established conditions explicitly depend on the upper and lower bounds of asynchronous switching delays. An alternative approach is proposed to decouple the bilinear problems of the control synthesis conditions. Convex optimization algorithms are also proposed based on the established conditions to determine the minimum l₂-gain performance. Two numerical examples are provided to illustrate the effectiveness of the proposed method, demonstrating significant improvement over the existing results.     

Standard H∞ performance of switched delay systems under minimum dwell time switching

This paper investigates the standard H_∞ performance for a class of switched linear systems with time-varying delay in the framework of the delay-dependent/delay-independent minimum dwell time. For the studied systems, we first construct two types of multiple time-varying Lyapunov functionals, and then obtain the sufficient conditions by restricting the decay of the Lyapunov functional of the active subsystem and forcing “energy” of the overall switched system to decrease at switching instants by the proposed Lyapunov functionals to guarantee standard L₂-gain performance meanwhile ensuring their internal stability with minimum dwell time switching. Finally, two examples are presented to illustrate the effectiveness of the proposed results.     

Incremental H∞ performance for a class of stochastic switched nonlinear systems

In this paper, we investigate the incremental H_∞ performance problem for a class of stochastic switched nonlinear systems by using a state-dependent switching law and the maximum and minimum dwell time approach. By resorting to the state-dependent switching law, some sufficient conditions are provided to cope with the incremental H_∞ performance problem, which can be applied even if all subsystems are unstable. Then, based on the maximum and minimum dwell time scheme, the incremental H_∞ performance problem to be solvable is derived for two cases: one is all subsystems are incrementally globally asymptotically stable in the mean(IGASiM), another is both IGASiM subsystems and unstable subsystems coexist. When all subsystems are IGASiM, the stochastic switched nonlinear system is IGASiM and possesses a incremental L₂-gain under given conditions. When both IGASiM subsystems and unstable subsystems coexist, if the activation time ratio between IGASiM subsystems and unstable ones is not less than a specified constant, the sufficient conditions for the incremental H_∞ performance of the stochastic switched nonlinear system are given. Two numerical examples are given to illustrate the validity of methods proposed.     

Mixed H∞ and passive control for a class of nonlinear switched systems with average dwell time via hybrid control approach

This paper investigates the mixed H_∞ and passive control problem for a class of nonlinear switched systems based on a hybrid control strategy. To solve this problem, firstly, using the Takagi–Sugeno (T–S) fuzzy model to approximate every nonlinear subsystem, the nonlinear switched systems are modeled as the switched T–S fuzzy systems. Secondly, the hybrid controllers are used to stabilize the switched T–S fuzzy systems. The hybrid controllers consist of dynamic output-feedback controllers for every subsystem and state updating controllers at the switching instant. Thirdly, a new performance index is proposed for switched systems. This new performance index can be viewed as the mixed weighted H_∞ and passivity performance. Based on this new performance index, the weighted H_∞ control problem and the passive control problem for switched T–S fuzzy systems via the hybrid control strategy are solved in a unified framework. Together the multiple Lyapunov functions (MLFs) approach with the average dwell time (ADT) technique, new design conditions for the hybrid controllers are obtained. Under these conditions, the closed-loop switched T–S fuzzy systems are globally uniformly asymptotically stable with a prescribed mixed H_∞ and passivity performance index. Moreover, the desired hybrid controllers can be constructed by solving a set of linear matrix inequalities (LMIs). Finally, the effectiveness of the obtained results is illustrated by a numerical example.     

Output tracking control with L1-gain performance for positive switched systems

This paper concentrates on the output tracking control problem with L₁-gain performance of positive switched systems. We adopt the multiple co-positive Lyapunov functions technique and conduct the dual design of the controller and the switching signal. Through introducing a new state variable, which is not the output error, the output tracking control problem of the original system is transformed into the stabilization problem of the dynamics system of this new state. The proposed approach is still effective even the output tracking control problem of any subsystem is unsolvable. According to the state being available or not, we establish the solvability conditions of the output tracking control problem for positive switched systems, respectively. In the end, a number example demonstrates the validity of the presented results.     

Non-weighted H∞ performance for 2-D FMLSS switched system with maximum and minimum dwell time

This paper investigates the H_∞ performance of two-dimensional (2-D) switched system represented by Fornasini–Marchesini local state-space (FMLSS) model with maximum and minimum dwell time approach. By using the multiple Lyapunov function approach, and designing a set of switching signals subject to maximum and minimum dwell time characteristic, respectively, for all stable subsystems or both stable and unstable subsystems exist, we give the sufficient condition on exponential stability of the given switched system, and propose the sufficient condition which can guarantee that the given switched system is exponentially stable and has a specified H_∞ disturbance attenuation level γ. All the results obtained are on normal noise attenuation index of strictly non-weighted form, which are better than the existing results on weak one of weighted form from the physical point of view. Finally, numerical examples are presented to display the effectiveness of the proposed results.     

Decentralized event-triggered H∞ control for switched systems with network communication delay

This paper is concerned with the decentralized event-triggered H_∞ control for switched systems subject to network communication delay and exogenous disturbance. Depending on different physical properties, the system state is divided into multiple communication channels and decentralized sensors are employed to collect signals on these channels. Furthermore, decentralized event-triggering mechanisms (DETMs) with a switching structure are proposed to determine whether the sampled data needs to be transmitted. In particular, an improved data buffer is presented which can guarantee more timely utilization of the sampled data. Then, with the proposed DETMs and data buffer, a time-delay closed-loop switched system is developed. After that, sufficient conditions are presented to guarantee the H_∞ performance of the closed-loop switched system by utilizing the average dwell time and piecewise Lyapunov functional method. Since the event-triggered instants and the switching instants may stagger with each other, the influence of their coupling on the H_∞ performance analysis is systematically discussed. Subsequently, sufficient conditions for designing the event-triggered state feedback controller gains are provided. Finally, numerical simulations are given to verify the effectiveness of the proposed method.     

Asynchronous H∞ fixed-order filtering for LPV switched delay systems with mode-dependent average dwell time

This paper investigates the problem of robust H_∞ fixed-order filtering for a class of linear parameter-varying (LPV) switched delay systems under asynchronous switching that the system parameter matrices and the time delays are dependent on the real-time measured parameters. The so-called asynchronous switching means that there are time delays between the switching of filters and the switching of system modes. By constructing the parameter-dependent and mode-dependent Lyapunov-Krasovskii functional which is allowed to increase during the running time of active subsystem with the mismatched filter, and using the mode-dependent average dwell time (MDADT) switching method, the sufficient conditions for exponential stability and satisfying a novel weighted H_∞ criterion are derived. As there exist couplings between Lyapunov-Krasovskii functional matrices and system parameter matrices, we utilize slack matrices to decouple them. Based on the above results, a suitable weighted H_∞ fixed-order filter can be obtained in the form of the parameter linear matrix inequalities (PLMIs). By virtue of approximate basis function and gridding technique, the design of weighted H_∞ fixed-order filter can be transformed into the solution of the finite dimensional LMIs. Finally, a numerical example is presented to verify both the effectiveness and the low conservatism of the parameter-dependent and mode-dependent fixed-order filtering method proposed in this paper.     

Event-based weighted residual generator design via non-PDC scheme for fault diagnosis in T–S fuzzy systems

This paper is concerned with the event-based weighted residual generator design via non-parallel distribution compensation (PDC) scheme for fault diagnosis in discrete-time T–S fuzzy systems, under consideration of the imperfect premise matching membership functions. An event-triggered mechanism is firstly introduced to save communication resources, which leads to the premise variables of the system and observer to be asynchronous. Then, a fuzzy diagnostic observer with mismatched premise variables is designed to estimate the unmeasurable states of the system. Moreover, by using non-PDC method, a diagnostic observer-based weighted residual generator is established to improve the fault detection (FD) performance by using the information provided by each local system, in which the membership functions structure of the diagnostic observer and residual generator need not to be the same as the systems, and the L_∞/L₂ and L_∞ FD scheme is used to optimize the FD performance. Finally, two simulation results are provided to show the efficiency of the proposed non-PDC method.     

Stability and L1-gain analysis for switched positive T–S fuzzy systems under asynchronous switching

This paper is concerned with the exponential stability and L₁-gain analysis problem for switched positive T–S fuzzy systems under both time-varying delays and asynchronous switching. By permitting the increase of the designed multiple Lyapunov functionals during the running time of the activated subsystem, solvable conditions for the stability and L₁-gain are developed by adopting the mode-dependent average dwell time (MDADT) technique. The desired controllers guaranteeing the stability and the L₁-gain performance are designed based on the obtained solvable conditions. An example is given to demonstrate the effectiveness of the proposed methods.     

Hybrid anti-bump control for switched nonlinear systems with event-triggering under sampled-data-based switching

This paper addresses the $H_{\infty }$ hybrid anti-bump control for switched nonlinear systems with event-triggering via the interval type-2 (IT2) fuzzy model. A unified framework of anti-bump performance for switched nonlinear systems called hybrid anti-bump performance is established to attenuate sudden big hybrid bumps caused by both triggering and switching. Then, we design a sampled-data-based switching strategy, under which we only need to check the switching conditions at discrete sampling instants. By using the multiple Lyapunov–Krasovskii functional theory and the constructed switching law, sufficient conditions are made for the considered systems to be asymptotically stable with both $H_{\infty }$ performance and hybrid anti-bump performance. Moreover, the switching law, the event-triggered scheme, and the event-triggered controllers are jointly designed. Finally, an electro-hydraulic model is exploited to verify the applicability and effectiveness of our method.     

Robust non-fragile filtering for networked systems with distributed variable delays

This paper is concerned with the robust non-fragile filtering for a class of networked systems with distributed variable delays. We model such a complex delay system with an augmented switched system. For the filtering implementation uncertainty, a stochastic variable is employed to indicate random occurrence of the filter gain change, and a norm bound to measure the change size. The suitably weighted measurements are proposed for filter performance improvement, instead of direct use of the measurements themselves which may have significant delays and degrade the performance. With some improved stability and l₂ gain analysis for the switched systems, a new sufficient condition is obtained such that the filtering error system is exponentially stable in the mean square sense and achieves a prescribed _H∞$H_{\infty }$ performance level. A numerical example is given to show the effectiveness of the proposed design.     

Stability, L1-gain analysis and asynchronous L1-gain control of uncertain discrete-time switched positive linear systems with dwell time

In this paper, the stability, L₁-gain analysis and asynchronous L₁-gain control problems of uncertain discrete-time switched positive linear systems (DSPLSs) with dwell time are investigated. First, several convex and non-convex conditions on dwell time stability of DSPLSs with interval and polytopic uncertainties are presented, and the relation between these conditions is revealed. Then, via a switched dwell-time-dependent co-positive Lyapunov functions (SDTLFs) approach, convex sufficient conditions on L₁-gain analysis and asynchronous L₁-gain control of DSPLSs with interval uncertainties are derived. Meanwhile, via the switched parameter-dwell-time-dependent co-positive Lyapunov functions (SPDTLFs) approach, the L₁-gain analysis and asynchronous L₁-gain controller design problems of DSPLSs with polytopic uncertainties are also solved. The stability and L₁-gain analysis results are given in terms of linear programming (LP). The controller design results are presented in terms of bilinear programming (BP), which can be solved with the help of iterative algorithm. At last, both numerical and practical examples are provided to show the effectiveness of the results.     

Finite-time H∞ control of switched systems with mode-dependent average dwell time

This paper is concerned with finite-time _H∞$H_{\infty }$ control problem for a class of switched linear systems by using a mode-dependent average dwell time (MDADT) method. The switching signal used in this paper is more general than the average dwell time (ADT), in which each mode has its own ADT. By combining the MDADT and Multiple Lyapunov Functions (MLFs) technologies, some sufficient conditions, which can guarantee that the corresponding closed-loop system is finite-time bounded with a prescribed _H∞$H_{\infty }$ performance, are derived for the switched systems. Moreover, a set of mode-dependent dynamic state feedback controllers are designed. Finally, two examples are given to verify the validity of the proposed approaches.     

Robust H∞ filtering for switched stochastic systems under asynchronous switching

This paper investigates the problem of robust H_∞ filtering for switched stochastic systems under asynchronous switching. The so-called asynchronous switching means that the switching between the filters and system modes is asynchronous. The aim is to design a filter ensuring robust exponential mean square stability and a prescribed H_∞ performance level for the filtering error systems. Based on the average dwell time approach and piecewise Lyapunov functional technique, sufficient conditions for the existence of the robust H_∞ filter are derived, and the proposed filter can be obtained by solving a set of LMIs(linear matrix inequalities). Finally, a numerical example is given to show the effectiveness of the proposed approach.