Stabilization for a class of second-order switched systems with saturation constrains

This paper proposes a global stabilization method for a class of planar switched systems with input saturation constrains by using a state feedback and switching strategy. This method is proved to be effective by analyzing the characteristics of the trajectory of second-order linear systems with input saturation.

Interpolated Bumpless Transfer Control for Asynchronously Switched Linear Systems

This paper revisits the problem of bumpless transfer control(BTC) for discrete-time nondeterministic switched linear systems. The general case of asynchronous switching is considered for the first time in the field of BTC for switched systems. A new approach called interpolated bumpless transfer control(IBTC) is proposed, where the bumpless transfer controllers are formulated with the combination of the two adjacent modedependent controller gains, and are interpolated for finite steps once the switching is detected. In contrast with the existing approaches, IBTC does not necessarily run through the full interval of subsystems, as well as possesses the time-varying controller gains(with more flexibility and less conservatism) achieved from a control synthesis allowing for the stability and other performance of the whole switched system. Sufficient conditions ensuring stability and H_(∞) performance of the underlying system by IBTC are developed, and numerical examples verify the theoretical findings.

Finite-Time H∞ Control of Switched Nonlinear Systems under State-Dependent Switching

This paper investigates the finite-time H∞ control problem of switched nonlinear systems via state-dependent switching and state feedback control. Unlike the existing approach based on time-dependent switching strategy, in which the switching instants must be given in advance, the state-dependent switching strategy is used to design switching signals. Based on multiple Lyapunov-like functions method, several criteria for switched nonlinear systems to be finite-time H∞ control are derived. Finally, a numerical example with simulation results is provided to show the validity of the conclusions.

Error reachable set based stabilization of switched linear systems with bounded peak disturbances

This paper investigates the error reachable set based stabilization problem for a class of discrete-time switched linear systems with bounded peak disturbances under persistent dwell-time(PDT)constraint.A double-clockdependent control scheme is presented that can split the disturbed switched system into a nominal system and an error system,and assign to each system a controller scheduled by a clock.A necessary and sufficient convex stability criterion is presented for the nominal system,and is further extended to the stabilization controller design with a nominal clock.In the presence of bounded peak disturbances,another stabilization controller with an error clock is developed for the error system,with the purpose of‘‘minimizing’’the reachable set of the error system by the ellipsoidal techniques.It is demonstrated that the disturbed system is also globally exponentially stable in the sense of converging to an over approximation of the reachable set of the error system,i.e.,a union of a family of bounding ellipsoids,that can also be regarded as the cross section of a tube containing the trajectories of the disturbed system.Two numerical examples are provided to verify the effectiveness of the developed results.

Consensus problem of second-order multi-agent systems with time-varying communication delay and switching topology

Leader-following stationary consensus problem is investigated for the second-order multi-agent systems with timevarying communication delay and switching topology. Based on Lyapunov-Krasovskii functional and Lyapunov-Razumikhin functions respectively, consensus criterions in the form of linear matrix inequality （LMI） are obtained for the system with time-varying communication delays under static interconnection topology con- verging to the leader＇s states. Moreover, the delay-dependent consensus criterion in the form of LMI is also obtained for the system with time-invariant communication delay and switching topologies by constructing Lyapunov-Krasovskii functional. Numerical simulations present the correctness of the results.

Asynchronous Learning-Based Output Feedback Sliding Mode Control for Semi-Markov Jump Systems: A Descriptor Approach

This paper presents an asynchronous output-feed-back control strategy of semi-Markovian systems via sliding mode-based learning technique.Compared with most literature results that require exact prior knowledge of system state and mode information,an asynchronous output-feedback sliding sur-face is adopted in the case of incompletely available state and non-synchronization phenomenon.The holonomic dynamics of the sliding mode are characterized by a descriptor system in which the switching surface is regarded as the fast subsystem and the system dynamics are viewed as the slow subsystem.Based upon the co-occurrence of two subsystems,the sufficient stochastic admissibility criterion of the holonomic dynamics is derived by utilizing the characteristics of cumulative distribution functions.Furthermore,a recursive learning controller is formulated to guarantee the reachability of the sliding manifold and realize the chattering reduction of the asynchronous switching and sliding motion.Finally,the proposed theoretical method is substantia-ted through two numerical simulations with the practical contin-uous stirred tank reactor and F-404 aircraft engine model,respectively.

Lyapunov-Based Output Containment Control of Heterogeneous Multi-Agent Systems With Markovian Switching Topologies and Distributed Delays

This paper considers the mean square output containment control problem for heterogeneous multi-agent systems(MASs)with randomly switching topologies and nonuniform distributed delays.By modeling the switching topologies as a continuous-time Markov process and taking the distributed delays into consideration,a novel distributed containment observer is proposed to estimate the convex hull spanned by the leaders'states.A novel distributed output feedback containment controller is then designed without using the prior knowledge of distributed delays.By constructing a novel switching Lyapunov functional,the output containment control problem is then solved in the sense of mean square under an easily-verifiable sufficient condition.Finally,two numerical examples are given to show the effectiveness of the proposed controller.

Admissibility analysis and control synthesis for switched linear singular systems

The problem of admissibility analysis and control synthesis of discrete-time switched linear singular （SLS） systems for arbitrary switching laws is solved. By using the switched Lyapunov function approach, some new sufficient conditions under which the SLS system is admissible for arbitrary switching laws are derived in terms of linear matrix inequalities （LMIs）. Based on the admissibility results, control synthesis is then to design switched state feedback and static output feedback controllers, guaranteeing that the resulting closed-loop system is admissible. The presented results can be viewed as the extensions of previous works on switched Lyapunov function approach from the regular switched systems to singular switched cases. Examples are provided to demonstrate the reduced conservatism and effectiveness of the proposed conditions.

A switched system approach to stabilization of networked control systems

A switched system approach is proposed to model networked control systems （NCSs） with communication constraints. This enables us to apply the rich theory of switched systems to analyzing such NCSs. Sufficient conditions are presented on the stabilization of NCSs. Stabilizing state/output feedback controllers can be constructed by using the feasible solutions of some linear matrix inequalities （LMIs）. The merit of our proposed approach is that the behavior of the NCSs can be studied by considering switched system without augmenting the system. A simulation example is worked out to illustrate the effectiveness of the proposed approach.

H-infinity control for switched and impulsive singular systems

A new model of dynamical systems is proposed which consists of singular systems with impulsive effects, i.e., switched and impulsive singular systems （SISS）. By using the switched Lyapunov functions method, a sufficient condition for the solvability of the H-infinity control problem for SISSs is given which generalizes the H-infinity control theory for singular systems to switched singular systems with impulsive effects. Then the sufficient condition of solvablity of the H-infinity control problem is presented in terms of linear matrix inequalities. Finally, the effectiveness of the developed aooroach for switched and imoulsive singular svstems is illustrated by a numerical example.

Quadratic Stabilization of Switched Uncertain Linear Systems: A Convex Combination Approach

We consider quadratic stabilization for a class of switched systems which are composed of a finite set of continuoustime linear subsystems with norm bounded uncertainties. Under the assumption that there is no single quadratically stable subsystem, if a convex combination of subsystems is quadratically stable, then we propose a state-dependent switching law, based on the convex combination of subsystems, such that the entire switched linear system is quadratically stable. When the state information is not available, we extend the discussion to designing an outputdependent switching law by constructing a robust Luenberger observer for each subsystem.

Cluster consensus of second-order multi-agent systems via pinning control

This paper investigates the cluster consensus problem for second-order multi-agent systems by applying the pinning control method to a small collection of the agents. Consensus is attained independently for different agent clusters according to the community structure generated by the group partition of the underlying graph and sufficient conditions for both cluster and general consensus are obtained by using results from algebraic graph theory and the LaSalle Invariance Principle. Finally, some simple simulations are presented to illustrate the technique.

Control of switched systems with actuator saturation

This paper is concerned with controller synthesis for linear switched systems with actuator saturation. Based on common Lyapunov function technique and multiple-Lyapunov function technique, two methods for designing state feedback controller are proposed respectively in terms of linear matrix inequalities for the switched systems with saturation. An approach on enlarging the attractive domain is then investigated, The application of the presented approach is illustrated finally by a numerical example.

Eigenstructure assignment in a class of second-order dynamic systems

Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of secondorder dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop eigenvector matrix and the feedback gains are established based on two simple Smith form reductions. The approach utilizes directly the original system data and involves manipulations only on n-dimensional matrices. Furthermore, it reveals all the degrees of freedom which can be further utilized to achieve additional system specifications. An example shows the effect of the proposed approach.

Minimum Dwell Time for Global Exponential Stability of a Class of Switched Positive Nonlinear Systems

This paper will investigate global exponential stability analysis for a class of switched positive nonlinear systems under minimum dwell time switching, whose nonlinear functions for each subsystem are constrained in a sector field by two odd symmetric piecewise linear functions and whose system matrices for each subsystem are Metzler. A class of multiple time-varying Lyapunov functions is constructed to obtain the computable sufficient conditions on the stability of such switched nonlinear systems within the framework of minimum dwell time switching.All present conditions can be solved by linear/nonlinear programming techniques. An example is provided to demonstrate the effectiveness of the proposed result.

Delay-dependent stability and stabilization of a class of linear switched time-varying delay systems

The stability and stabilization of a class of linear switched time-varying delay systems are investigated. A piecewise quadratic Lyapunov function （PWQLF） is constructed and is used to obtain the stability conditions based on the linear matrix inequalities （LMIs）. The stabilizing controller for this class of system is then designed and the solution of the desired controller can be obtained by a cone complementary linearization algorithm. Numerical examples are provided to illustrate the less conservativeness of the new stability and the validity of the controller design procedures.

Guaranteed cost control with constructing switching law of uncertain discrete-time switched systems

A guaranteed cost control problem for a class of linear discrete-time switched systems with norm-bounded uncertainties is considered in this article. The purpose is to construct a switching rule and design a state feedback control law, such that, the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties under the constructed switching rule. A sufficient condition for the existence of guaranteed cost controllers and switching rules is derived based on the Lyapunov theory together with the linear matrix inequality （LMI） approach. Furthermore, a convex optimization problem with LMI constraints is formulated to select the suboptimal guaranteed cost controller. A numerical example demonstrates the validity of the proposed design approach.

On stability of switched linear systems with perturbed switching paths

This paper addresses the stability issue of switched linear systems with perturbed switching paths. First, by introducing the notions of child-path and parent-path, we are able to define the distance between two switching paths by means of their switching matrices chains. Next, we present the nice properties of the defined distance. Then, a stability criterion is presented for a class of switched linear systems with perturbed switching paths. Finally, an illustrative example is presented to verify the effectiveness of the approach.

H∞ Tracking Control for Switched LPV Systems With an Application to Aero-Engines

This paper focuses on the H_∞ model reference tracking control for a switched linear parameter-varying(LPV)model representing an aero-engine. The switched LPV aeroengine model is built based on a family of linearized models.Multiple parameter-dependent Lyapunov functions technique is used to design a tracking control law for the desirable H_∞ tracking performance. A control synthesis condition is formulated in terms of the solvability of a matrix optimization problem.Simulation result on the aero-engine model shows the feasibility and validity of the switching tracking control scheme.

Critical dwell time of switched linear systems

In this paper, we consider the relation between the switching dwell time and the stabilization of switched linear control systems. First of all, a concept of critical dwell time is given for switched linear systems without control inputs, and the critical dwell time is taken as an arbitrary given positive constant for a switched linear control systems with controllable switching models. Secondly, when a switched linear system has many stabilizable switching models, the problem of stabilization of the overall system is considered. An on-line feedback control is designed such that the overall system is asymptotically stabilizable under switching laws which depend only on those of uncontrollable subsystems of the switching models. Finally, when a switched system is partially controllable （While some switching models are probably unstabilizable）, an on-line feedback control and a cyclic switching strategy are designed such that the overall system is asymptotically stabilizable if all switching models of this uncontrollable subsystems are asymptotically stable. In addition, algorithms for designing switching laws and controls are presented.