Stability of Switched Positive Descriptor Systems with Average Dwell Time Switching

In this paper, the problems of stability for a class of switched positive descriptor systems(SPDSs)with average dwell time(ADT) switching are investigated. First, based on the equivalent switched system and the properties of the projector matrix, sufficient stabilities are given for the underlying systems in both continuoustime and discrete-time contexts. Then, a sufficient stability condition for the SPDS with both stable and unstable subsystems is obtained. The stability results for the SPDSs are represented in terms of a set of linear programmings(LPs) by the multiple linear co-positive Lyapunov function(MLCLF) approach. Finally, three numerical examples are given to illustrate the effectiveness of the obtained theoretical results.

Stabilization of switched linear systems under asynchronous switching subject to admissible edge-dependent average dwell time

The problem of stabilizing switched linear systems under asynchronous switching is addressed.The admissible edge-dependent average dwell time method is applied to design a switching signal that comprises slow admissible edge-dependent average dwell time and fast admissible edge-dependent average dwell time.Under this switching signal,the restriction that the maximum delay of asynchronous switching is known in advance is removed.The constructed Lyapunov function is associated with both the system mode and controller mode.The stabilization criteria and the corresponding algorithm are presented to obtain the controller gains and to design the switching signal.Finally,two examples are given to demonstrate the effectiveness of the proposed results.

Pose Synchronization of Multiple Rigid Bodies Under Average Dwell Time Condition

This paper considers the pose synchronization problem of a group of moving rigid bodies under switching topologies where the dwell time of each topology may has no nonzero lower bound. The authors introduce an average dwell time condition to characterize the length of time intervals in which the graphs are connected. By designing distributed control laws of angular velocity and linear velocity,the closed-loop dynamics of multiple rigid bodies with switching topologies can be converted into a hybrid dynamical system. The authors employ the Lyapunov stability theorem, and show that the pose synchronization can be reached under the average dwell time condition. Moreover, the authors investigate the pose synchronization problem of the leader-following model under a similar average dwell time condition. Simulation examples are given to illustrate the results.

Robust exponential stability of uncertain discretetime impulsive switching systems with state delay

A new class of hybrid impulsive and switching models are introduced and their robust exponential stability and control synthesis are addressed. The proposed switched system is composed of stable subsystems and unstable subsystems, which not only involves state delay and norm-bounded time-varying parameter uncertainties, but also contains the impulsive switching effects between the subsystems. Based on the extension of the system dimension and the concept of average dwell time, a kind of practically useful switching rule is presented which guarantees the desired robust exponential stability. A switched state feedback controller is also given.

H_-/H_∞ fault detection filter design for interval time-varying delays switched systems

The problem of the robust fault detection filter design for time-varying delays switched systems is considered in the framework of mixed H-/H∞. Firstly, the weighted H∞ performance index is utilized as the robustness performance, and the H- index is used as the sensitivity performance for obtaining the robust fault detection filter. Then a novel multiple Lyapunov-Krasovskii function is proposed for deriving sufficient existence conditions of the robust fault detection filter based on the average dwell time technique. By introducing slack matrix variable, the coupling between the Lyapunov matrix and system matrix is removed, and the conservatism of results is reduced. Based on the robust fault detection filter, residual is generated and evaluated for detecting faults. In addition, the results of this paper are dependent on time delays,and represented in the form of linear matrix inequalities. Finally,the simulation example verifies the effectiveness of the proposed method.

Event-Triggered Finite-Time <i>H</i>_∞Control for Switched Stochastic Systems

This paper investigates the problem of event-triggered finite-time H∞ control for a class of switched stochastic systems. The main objective of this study is to design an event-triggered state feedback H∞ controller such that the resulting closed-loop system is finite-time bounded and satisfies a prescribed H∞ level in some given finite-time interval. Based on stochastic differential equations theory and average dwell time approach, sufficient conditions are derived to ensure the finite-time stochastic stability with the prescribed H∞ performance for the relevant closed-loop system by employing the linear matrix inequality technique. Finally, the desired state feedback H∞ controller gain matrices can be expressed in an explicit form.

Robust fault detection for delta operator switched fuzzy systems with bilateral packet losses

Considering packet losses, time-varying delay, and parameter uncertainty in the switched fuzzy system, this paper designs a robust fault detection filter at any switching rate and analyzes the H∞ performance of the system. Firstly, the Takagi-Sugeno(T-S) fuzzy model is used to establish a global fuzzy model for the uncertain nonlinear time-delay switched system,and the packet loss process is modeled as a mathematical model satisfying Bernoulli distribution. Secondly, through the average dwell time method and multiple Lyapunov functions, the exponentially stable condition of the nonlinear network switched system is given. Finally, specific parameters of the robust fault detection filter can be obtained by solving linear matrix inequalities(LMIs). The effectiveness of the method is verified by simulation results.

Exponential stability of impulsive jump linear systems with Markov process

The exponential stability is investigated for a class of continuous time linear systems with a finite state Markov chain form process and the impulsive jump at switching moments. The conditions, based on the average dwell time and the ratio of expectation of the total time running on all unstable subsystems to the expectation of the total time running on all stable subsystems,assure the exponential stability with a desired stability degree of the system irrespective of the impact of impulsive jump. The uniformly bounded result is realized for the case in which switched system is subjected to the impulsive effect of the excitation signal at some switching moments.

Robust H-infinity integral sliding mode control for a class of uncertain switched nonlinear systems

This paper develops a new method to deal with the robust H-infinity control problem for a class of uncertain switched nonlinear systems by using integral sliding mode control.A robust H-infinity integral sliding surface is constructed such that the sliding mode is robust stable with a prescribed disturbance attenuation level γ for a class of switching signals with average dwell time.Furthermore,variable structure controllers are designed to maintain the state of switched system on the sliding surface from the initial time.A numerical example is given to illustrate the effectiveness of the proposed method.

Control synthesis of linear distributed parameter switched systems

The control synthesis for switched systems is extended to distributed parameter switched systems in Hilbert space. Based on semigroup and operator theory, by means of multiple Lyapunov method incorporated average dwell time approach, sufficient con- ditions are derived in terms of linear operator inequalities frame- work for distributed parameter switched systems. Being applied to one dimensional heat propagation switched systems, these lin- ear operator inequalities are reduced to linear matrix inequalities subsequently. In particular, the state feedback gain matrices and the switching law are designed, and the state decay estimate is explicitly given whose decay coefficient completely depends on the system＇s parameter and the boundary condition. Finally, two numerical examples are given to illustrate the proposed method.

Exponential H_∞ filtering analysis for discrete-time switched neural networks with random delays using sojourn probabilities

This paper is concerned with the exponential H_∞ filtering problem for a class of discrete-time switched neural networks with random time-varying delays based on the sojourn-probability-dependent method. Using the average dwell time approach together with the piecewise Lyapunov function technique, sufficient conditions are proposed to guarantee the exponential stability for the switched neural networks with random time-varying delays which are characterized by introducing a Bernoulli stochastic variable.Based on the derived H_∞ performance analysis results, the H_∞ filter design is formulated in terms of Linear Matrix Inequalities(LMIs). Finally, two numerical examples are presented to demonstrate the effectiveness of the proposed design procedure.

Robust stability analysis of switched uncertain systems with multiple time-varying delays and actuator failures

In this paper,the robust stability issue of switched uncertain multidelay systems resulting from actuator failures is considered.Based on the average dwell time approach,a set of suitable switching signals is designed by using the total activation time ratio between the stable subsystem and the unstable one.It is first proven that the resulting closed-loop system is robustly exponentially stable for some allowable upper bound of delays if the nominal system with zero delay is exponentially stable under these switching laws.Particularly,the maximal upper bound of delays can be obtained from the linear matrix inequalities.At last,the effectiveness of the proposed method is demonstrated by a simulation example.

Analysis of robust stability for switched systems with multiple time-delays

The sufficient conditions of delay-dependent exponential stability for switched systems and robust exponential stability for uncertain switched systems with two time-delays are presented by using average dwell time method and free-weighting matrix method.The interaction between different time-delays is considered.The sufficient conditions do not need that every subsystem is stable.The designed methods of the switching law are also given.The sufficient conditions are given in the form of linear matrix inequalities that can be solved easily.The result is proven to be valid by the simulation at last.

Guaranteed Cost Finite-Time Control of Fractional-Order Nonlinear Positive Switched Systems with D-Perturbations via MDADT

This paper is concerned with the problem of guaranteed cost finite-time control of fractionalorder nonlinear positive switched systems (FONPSS) with D-perturbation. Firstly, the proof of the positivity of FONPSS with D-perturbation is given, the definition of guaranteed cost finite-time stability is firstly given in such systems. Then, by constructing linear copositive Lyapunov functions and using the mode-dependent average dwell time (MDADT) approach, a static output feedback controller is constructed, and sufficient conditions are derived to guarantee that the corresponding closed-loop system is guaranteed cost finite-time stable (GCFTS). Such conditions can be easily solved by linear programming. Finally, an example is provided to illustrate the effectiveness of the proposed method.

Exponential stability and L_(2) gain analysis of switched distributed parameter systems with time delay

The present paper is concerned with stability and L_(2) gain analysis of switched distributed parameter system(SDPS)with time delay.First,exponential stability is discussed,and the state decay estimate of the system is explicitly given by using linear matrix inequalities(LMIs)incorporating with the average dwell time(ADT)method.Second,L_(2) gain analysis is also studied.At last,illustrative examples are given to show the effectiveness of the proposed method.The main contribution of the paper is:some criteria of exponential stability and L_(2) gain for multiple-input multiple-output(MIMO)switched PDE are developed in the form of LMIs and ADT signal for the first time.The advantage of the work is we generalize the application range of the related research.The proposed method is expected to provide an effective tool for stability and H∞control analysis of SDPS.

Exponential stability of nonlinear impulsive switched systems with stable and unstable subsystems

Exponential stability and robust exponential stability relating to switched systems consisting of stable and unstable nonlinear subsystems are considered in this study.At each switching time instant,the impulsive increments which are nonlinear functions of the states are extended from switched linear systems to switched nonlinear systems.Using the average dwell time method and piecewise Lyapunov function approach,when the total active time of unstable subsystems compared to the total active time of stable subsystems is less than a certain proportion,the exponential stability of the switched system is guaranteed.The switching law is designed which includes the average dwell time of the switched system.Switched systems with uncertainties are also studied.Sufficient conditions of the exponential stability and robust exponential stability are provided for switched nonlinear systems.Finally,simulations show the effectiveness of the result.

Input-to-State Stability of Switched Nonlinear Delay Systems Based on a Novel Lyapunov-Krasovskii Functional Method

In this paper, the input-to-state stability （ISS） analysis is addressed for switched nonlinear delay systems. By introducing a novel Lyapunov-Krasovskii functional with indefinite derivative and the merging switching signal techniques, some new- criteria are established for switched nonlinear delay systems under asynchronous switching, which extends the existing results to the nonlinear systems with switching rules and delays. The ISS problem is also considered under synchronous switching for switched nonlinear systems by employing the similar techniques. Finally, a nonlinear delay model is provided to show the effectiveness of the proposed results.

Robust dynamic output feedback control for switched polytopic systems under asynchronous switching

The robust controller design problem for switched polytopic systems under asynchronous switching is addressed.These systems exist in many aviation applications, such as dynamical systems involving rapid variations.A switched polytopic system is established to describe the highly maneuverable technology vehicle within the full flight envelope and a robust dynamic output feedback control method is designed for the switched polytopic system.Combining the Lyapunov-like function method and the average dwell time method, a sufficient condition is derived for the switched polytopic system with asynchronous switching and data dropout to be globally,uniformly and asymptotically stable in terms of linear matrix inequality.The robust dynamic output feedback controller is then applied to the highly maneuverable technology vehicle to illustrate the effectiveness of the proposed approach.The simulation results show that the angle of attack tracking performance is acceptable over the time history and the control surface responses are all satisfying along the full flight trajectory.

Robust Exponential Stability of Switched Interval Interconnected Systems with Unbounded Delay

In this paper, a class of switched interval interconnected systems with unbounded delay were investigated. On the assumption that the interconnected functions of the systems satisfied the global Lipschitz condition, by using vector Lyapunov methods and M-matrix theory, the integrodifferential inequalities with unbounded delay were constructed. By the stability analysis of the integrodifferential inequalities, the sufficient conditions to ensure the robust exponential stability of the interval interconnected systems were obtained. By using average dwell time approach, conditions for guaranteeing the robust exponential stability of the switched delay interval interconnected systems were derived.Finally, two numerical examples were given to illustrate the correction and effectiveness of the proposed theory.

Observer-based fault detection for switched systems with all unstable subsystems

This paper deals with the fault detection observer design problem for switched system with all modes unstable.First,the error system model is presented.With the consideration of the instability caused by the unobservable condition of(Ai,Ci),a switching signal is obtained via average dwell time method and discretised Lyapunov function.By means of linear matrix inequalities,sufficient conditions pledging exponential stability and H∞performance are proposed.Through transferring the observer design problem into H∞performance analysis,proper observer gain is obtained via solving these LMIs.In the end,the validity of the proposed Luenberger observer is verified by an example.