Stability analysis of linear/nonlinear switching active disturbance rejection control based MIMO continuous systems

In this paper,a linear/nonlinear switching active disturbance rejection control(SADRC)based decoupling control approach is proposed to deal with some difficult control problems in a class of multi-input multi-output(MIMO)systems such as multi-variables,disturbances,and coupling,etc.Firstly,the structure and parameter tuning method of SADRC is introduced into this paper.Followed on this,virtual control variables are adopted into the MIMO systems,making the systems decoupled.Then the SADRC controller is designed for every subsystem.After this,a stability analyzed method via the Lyapunov function is proposed for the whole system.Finally,some simulations are presented to demonstrate the anti-disturbance and robustness of SADRC,and results show SADRC has a potential applications in engineering practice.

Stability and Stabilization of Block-cascading Switched Linear Systems

The main purpose of this paper is to investigate the problem of quadratic stability and stabilization in switched linear systems using reducible Lie algebra. First, we investigate the structure of all real invariant subspaces for a given linear system. The result is then used to provide a comparable cascading form for switching models. Using the common cascading form, a common quadratic Lyapunov function is （QLFs） is explored by finding common QLFs of diagonal blocks. In addition, a cascading Quaker Lemma is proved. Combining it with stability results, the problem of feedback stabilization for a class of switched linear systems is solved.

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.

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.

Asynchronous Observer Design for Switched Linear Systems: A Tube-Based Approach

This paper proposes a tube-based method for the asynchronous observation problem of discrete-time switched linear systems in the presence of amplitude-bounded disturbances.Sufficient stability conditions of the nominal observer error system under mode-dependent persistent dwell-time(MPDT)switching are first established. Taking the disturbances into account, a novel asynchronous MPDT robust positive invariant(RPI) set and an asynchronous MPDT generalized RPI(GRPI)set are determined for the difference system between the nominal and disturbed observer error systems. Further, the global uniform asymptotical stability of the observer error system is established in the sense of converging to the asynchronous MPDT GRPI set, i.e., the cross section of the tube of the observer error system. Finally, the proposed results are validated on a space robot manipulator example.

Chaotification for switched linear systems with controllers

This paper shows that two or more switched linear systems can generate chaotic dynamical behaviors by an appropriate switching rule as they at least consist of a controllable system and an unstable system with the expanding property. According to the results in the reference （Xie, L. L., Zhou, Y., and Zhao, Y. Criterion of chaos for switched linear systems with antrollers. International Journal of Bifurcation and Chaos, 20（12）, 4105-4109 （2010））, a nonlinear feedback gain is needed to generate chaotic dy- namics. A linear feedback control is usually used to approximate the nonlinear one for simulation. In order to obtain the exact control, as a main result of this paper, the con- troller is constructed by Russell＇s result, and a block diagram is included to interpret the realization of the controller. Numerical simulations are given to illustrate the generated chaotic dynamical behavior of the switched linear systems with some parameters and show the effects of the constructed controller.

Stabilization of Slowly Varying Switched Linear Systems

The stabilization problem of systems that switch among a finite set of slowly varying linear systems with arbitrary switching frequency is discussed.It is shown that if the entries of the pointwise stabilizing feedback gain matrix are continuously differentiable functions of the entries of the system coefficient matrices,then the closed-loop system is uniformly asymptotically stable if the rate of time variation of the system coefficient matrices is sufficiently small.

Optimal fault detection for a class of discrete-time switched linear systems

This paper deals with the problem of optimal fault detection filter （FDF） design for a class of discrete-time switched linear systems under arbitrary switching. By using an observer-based FDF as a residual generator, the design of the FDF is formulated into an optimization problem through maximizing the H_/H∞ or H∞/H∞ performance index. With the aid of an operator optimization method, it is shown that a mode-dependent unified optimal solution can be derived by solving a coupled Riccati equation. A numerical example is given to show the effectiveness of the proposed method.

Robust H_∞ output feedback controller design for linear uncertain discrete-time switched systems via state reset

This paper studies the problem of robust H∞ output feedback controller via state-reset for linear uncertain discrete-time switched systems. Using multiple Lyapunov functions,we address an output feedback controller under arbitrary switching signals,in which an H∞ performance is required. The condition is shown in the form of linear matrix inequalities (LMI). Finally,a numerical example shows the feasibility of the designed controller and illustrates that the new sufficient condition has lower conservation and more optimized H∞ tfperformance.

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.

Identification algorithm of switched systems based on generalized auxiliary model

For switched linear system with colored measurement noises,the identification difficulties of this system are that there exist unknown switching information,unknown middle variables and noise terms in the information vector.For the mentioned issues,the fuzzy clustering and the multi-innovation recursive identification algorithm are used to deal with these problems.Firstly,the mode detection is transformed into the detection of membership degree values confirmed by the fuzzy clustering method,and the problem of mode detection is solved by judgment and decision of the fuzzy membership values.Moreover,the multi-innovation recursive identification algorithm based on the generalized auxiliary model is proposed to estimate the parameters of the switched linear system with colored noises.Finally,the effectiveness of the proposed method is verified by the results of the simulation example.

Observer-based robust H-infinity control for uncertain switched systems

The problem of observer-based robust H-infinity control is addressed for a class of linear discrete-time switched systems with time-varying norm-bounded uncertainties by using switched Lyapunov function method. None of the individual subsystems is assumed to be robustly H-infinity solvable. A novel switched Lypunov function matrix with diagonal-block form is devised to overcome the difficulties in designing switching laws. For robust H-infinity stability analysis, two linear-matrix-inequality-based sufficient conditions are derived by only using the smallest region function strategy if some parameters are preselected. Then, the robust H-infinity control synthesis is studied using a switching state feedback and an observer-based switching dynamical output feedback. All the switching laws are simultaneously constructively designed. Finally, a simulation example is given to illustrate the validity of the results.

Delay-dependent robust H∞ control for a class of uncertain switched systems with time delay

For linear switched system with both parameter uncertainties and time delay, a delay-dependent sufficient condition for the existence of a new robust H∞ feedback controller was formulated in nonlinear matrix inequalities solvable by an LMI-based iterative algorithm. Compared with the conventional state-feedback controller, the proposed controller can achieve better robust control performance since the delayed state is utilized as additional feedback information and the parameters of the proposed controllers are changed synchronously with the dynamical characteristic of the system. This design method was also extended to the case where only delayed state is available for the controller. The example of balancing an inverted pendulum on a cart demonstrates the effectiveness and applicability of the proposed design methods.

Optimal design of linear switched reluctance motor for sea wave power generation

The switchless reluctance motor’s non-permanent magnet structure design ensures its high reliability in the marine environment;thus,it is a feasible solution for the generator of a sea wave power generation system.However,the corresponding thrust density and efficiency remain insufficient.This study focused on a new type of flat linear switched reluctance motor(LSRM),using the finite element software to establish a structural model,and optimized the design with the goal of improving the efficiency and energy density.The entropy method was adopted for sensitivity stratification to objectively select weights to avoid the influence of subjectively selected different proportional weights on the optimization results.Based on the entropy method,the sensitivity of different structural parameters was stratified,and the simulated annealing algorithm,response surface method,and single parameter scanning method were combined for optimization.Finally,the optimal structural size parameters of the motor were determined.Based on the two-dimensional finite element method,to simulate the electromagnetic performance of the reluctance motor under different operating conditions,such as thrust,loss,and efficiency,changes in motor performance before and after optimization were compared to verify the high power generation efficiency and energy density of the optimized linear motor.

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅱ)—SINGLE TIME_DELAY CASE

The controllability for switched linear systems with time_delay in controls is first investigated. The whole work contains three parts. This is the second part. The definition and determination of controllability of switched linear systems with single time_delay in control functions is mainly investigated. The sufficient and necessary conditions for the one_periodic, multiple_periodic controllability of periodic_type systems and controllability of periodic systems are presented, respectively.

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅲ)—MULTIPLE TIME_DELAY CASE

The controllability for switched linear systems with time_delay in controls is first investigated. The whole work contains three parts. This is the third part. The definition and determination of controllability of switched linear systems with multiple time_delay in control functions is mainly investigated. The sufficient and necessary conditions for the one_periodic, multiple_periodic controllability of periodic_type systems and controllability of aperiodic systems are presented,respectively. Finally, the case of distinct delays is discussed, it is shown that the controllability is independent of the size of delays.

Four-quadrant Force Control with Minimal Ripple for Linear Switched Reluctance Machines

Linear switch reluctance machine(LSRM)has been tried to act as an alternative generator for direct drive linear wave energy converter(WEC).Many researchers have proposed new topologies of LSRM to improve the power density,efficiency and reliability.However,the control methods for LSRM applied in direct drive WEC have been paid little attention,especially control methods considering the wave energy generator operating characteristics.In this paper,according to the generator control requirements of the direct drive WEC,force control algorithm for LSRM operating in four quadrants without a speed closed loop is put forward.The force ripple of LSRM is suppressed using force sharing function method.The four-quadrant control is easy to realize requiring only phase currents information.Simulation results validate the proposed method and indicate that LSRM is able to be used as the generator for direct drive WEC.

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅰ)—BASIC PROPERTIES AND PRELIMINARY RESULTS

The controllability for switched linear system with time_delay in controls was first investigated. The whole work contains three parts. This is the first part, including problem formulation and some preliminaries. Firstly, the mathematical model of switched linear systems with time_delay in control functions was presented. Secondly, the concept of column space, cyclic invariant subspace and generalized cyclic invariant subspace were introduced. And some basic properties, such as separation lemma, were presented. Finally, a basic lemma was given to reveal the relation between the solution set of a centain integral equations and the generalized cyclic invariant subspace. This lemma will play an important role in the determination of controllability. All these definitions and lemmas are necessary research tools for controllability analysis.

QoS aware routing and wavelength allocation in optical burst switching networks using differential evolution optimization

The issue of burst losses imposes a constraint on the development of Optical Burst Switching （OBS） networks. Heavy burst losses strongly affect the Quality of Service （QoS） intended by end users. This article presents a QoS aware Routing and Wavelength Allocation （RWA） technique for burst switching in OBS networks. The RWA problem is modeled as a bi-objective Integer Linear Programming （ILP） problem, where objective functions are based on minimizing the number of wavelengths used and the number of hops traversed to fulfill the burst transmission requests for a given set of node pairs. The ILP model is solved using a novel approach based on a Differential Evolution （DE） algorithm. Analytical results show that the DE algorithm provides a better performance compared to shortest path routing, which is a widely accepted routing strategy for OBS networks.

Review of Linear Switched Reluctance Motor Designs for Linear Propulsion Applications

Linear switched reluctance motor(LSRM)and its applications in different industries have been an interesting research topic for the past few years.LSRMs have proved to be a suitable alternative in a variety of applications requiring linear motion.However,its use is not that popular which instigated an active interest in the evolution of newer LSRM configurations.Enhancement in its propulsion force along with the reduction in force ripples,weight,acoustic noise,and vibration have been the main objectives in recently proposed LSRM designs.In this paper,recently proposed LSRM designs are reviewed and analyzed.The paper presents a one-stop introduction and a complete update to the designs,both in terms of qualitative and quantitative parameters.In addition,it takes into account the challenges in the implementation of these designs.Based on a detailed comparison of these designs as presented in this paper,an appropriate design can be chosen for a given application.