Research on controllability for a class of fractional-orderlinear control systems

The controllability for a class of fractional-order linear control systems is mainly investigated. The generalizations of the usual complete solution formulae of the fractional-order linear control systems are derived not only for time-invariant case but also for time-varying case. Several sufficient and necessary conditions for state controllability of such systems are established and the corresponding criteria for fractional-order time-invariant continuous-time systems are also obtained. The results obtained will be help for future study of fractional-order control systems.

LINEAR CONTROL SYSTEMS WITH TIME-LAG:CONTROLLABILITY AND LOCAL PARAMETRICAL IDENTIFIABILITY WITH EXTENSIONS IN PRE-HILBERT SPACES

Conditions are given for controllability, output controllability and local identifiabitity of a parametrization in a subset of of linear differential systems with time-lags.

ON THE ASYMPTOTIC ASSIGNMENT OF THE BOUNDS OF DECREASING RATE FOR A TIME-VARYING LINEAR CONTROL SYSTEM

In the paper the problem on the assignment of the bounds of decreasing rate for a time-varying linear control system is discussed. The sufficient and necessary condition for bounds of decreasing rate of a time-varying linear system to be assigned arbitrarily is presented. It is pointed out that for any given real number m, M, m<M, there exists a linear state feedback with time-varying gain matrix which makes the corresponding closed-loop system possess M and m as its upper bound and lower bound of the decreasing rate respectively. For the purposes of its application to system design the concept of the asymptotic assignment of the bounds of decreasing rate is also proposed. The method dealing with the asymptotic assignment is given too.

Criteria for Stability of Linear Control Systems

As it is well known, it is significant to know whether a matrix is an H-matrix or not in stability analysis of linear control systems. However, to distinguish H-matrices is difficult in real applications. In this paper, a practical extension of the sufficient conditions for H-matrices is investigated under some conditions. A larger scale of H-matrices which can be judged by the proposed method is shown by the numerical examples.

The Analysis of the Dynamic Equilibrium State in Linear Control System

This paper discusses not a point of equilibrium to free system,but a certain family of equilibrium state of dynami- cal system with inputs.This equilibrium state depends on the input,so it is called the dynamic equilibrium state.The expression of the dynamic equilibrium state can be given under some certain condition.With deductions and proofs in linear control system,es- tablish the expression of the dynamic equilibrium state in two cases,where the linear systems are nonsingular or singular.Also pre- sent the concept and the condition of the controllability of the dynamic equilibrium state.The controllability of the dynamic equilib- rium state is different from the controllability of the state to system,but these two are closely related.

EXACT LINEARIZATION BASED MULTIPLE-SUBSPACE ITERATIVE RESOLUTION TO AFFINE NONLINEAR CONTROL SYSTEM

To the optimal control problem of affine nonlinear system, based on differential geometry theory, feedback precise linearization was used. Then starting from the simulative relationship between computational structural mechanics and optimal control, multiple-substructure method was inducted to solve the optimal control problem which was linearized. And finally the solution to the original nonlinear system was found. Compared with the classical linearizational method of Taylor expansion, this one diminishes the abuse of error expansion with the enlargement of used region.

ROBUST CONTROL VIA STATE FEEDBACK FOR A CLASS OF UNCERTAIN BILINEAR SYSTEMS

This paper is concerned with the problem of designing a stabilizing controller for a class of uncertain bilinear systems. The uncertainties in the systems must satisfy the matching condition and their bounds should be known. The so-called improved approach for stability analysis of nonlinear system was used. Under some suitable assumptions a linear robust state feedback controller can be designed. At last, an illustrative example was demonstrated.

New trajectory linearization control for nonlinear systems undergoing harmonic disturbance

This paper presents a new trajectory linearization control scheme for a class of nonlinear systems subject to harmonic disturbance. It is supposed that the frequency of the disturbance is known, but the amplitude and the phase are unknown. A disturbance observer dynamics is constructed to estimate the harmonic disturbance, and then the estimation is used to implement a compensation control law to cancel the disturbance. By Lyapunov＇s direct method, a rigorous poof shows that the composite error of the closed-loop system can approach zero exponentially. Finally, the proposed method is illustrated by the application to control of an inverted pendulum. Compared with two existing methods, the proposed method demonstrates better performance in tracking error and response time.

Robust H_∞ Stabilization of Uncertain Linear Time-Delay System with Delayed/Undelayed State Feedback Controllers

This paper focuses on the H∞ controller design for linear systems with time-varying delays and norm-bounded parameter perturbations in the system state and control/disturbance. On the existence of delayed/undelayed full state feedback controllers, we present a sufficient condition and give a design method in the form of Riccati equation. The controller can not only stabilize the time-delay system, but also make the H∞ norm of the closed-loop system be less than a given bound. This result practically generalizes the related results in current literature.

Necessary and Suffcient Conditions for Distinguishability of Linear Control Systems

Distinguishability plays a crucial rule in studying observability of hybrid system such as switched system. Recently, for two linear systems, Lou and Si gave a condition not only necessary but also sufficient to the distinguishability of linear systems. However, the condition is not easy enough to verify. This paper will give a new equivalent condition which is relatively easy to verify.

Design of bounded feedback controls for linear dynamical systems by using common Lyapunov functions

For a linear dynamical system,we address the problem of devising a bounded feedback control,which brings the system to the origin in finite time.The construction is based on the notion of a common Lyapunov function.It is shown that the constructed control remains effective in the presence of small perturbations.

Research of robust adaptive trajectory linearization control based on T-S fuzzy system

A robust adaptive trajectory linearization control （RATLC） algorithm for a class of nonlinear systems with uncertainty and disturbance based on the T-S fuzzy system is presented. The unknown disturbance and uncertainty are estimated by the T-S fuzzy system, and a robust adaptive control law is designed by the Lyapunov theory. Irrespective of whether the dimensions of the system and the rules of the fuzzy system are large or small, there is only one parameter adjusting on line. Uniformly ultimately boundedness of all signals of the composite closed-loop system are proved by theory analysis. Finally, a numerical example is studied based on the proposed method. The simulation results demonstrate the effectiveness and robustness of the control scheme.

A new hyperchaotic system and its linear feedback control

This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system, studies some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter k. Furthermore, effective linear feedback control method is used to suppress hyperchaos to unstable equilibrium, periodic orbits and quasi-periodic orbits. Numerical simulations are presented to show these results.

Adaptive linear active disturbance-rejection control strategy reduces the impulse current of compressed air energy storage connected to the grid

The merits of compressed air energy storage(CAES)include large power generation capacity,long service life,and environmental safety.When a CAES plant is switched to the grid-connected mode and participates in grid regulation,using the traditional control mode with low accuracy can result in excess grid-connected impulse current and junction voltage.This occurs because the CAES output voltage does not match the frequency,amplitude,and phase of the power grid voltage.Therefore,an adaptive linear active disturbance-rejection control(A-LADRC)strategy was proposed.Based on the LADRC strategy,which is more accurate than the traditional proportional integral controller,the proposed controller is enhanced to allow adaptive adjustment of bandwidth parameters,resulting in improved accuracy and response speed.The problem of large impulse current when CAES is switched to the grid-connected mode is addressed,and the frequency fluctuation is reduced.Finally,the effectiveness of the proposed strategy in reducing the impact of CAES on the grid connection was verified using a hardware-in-the-loop simulation platform.The influence of the k value in the adaptive-adjustment formula on the A-LADRC was analyzed through simulation.The anti-interference performance of the control was verified by increasing and decreasing the load during the presynchronization process.

BLOCK DIAGONAL FORM AND BLOCK DIAGONAL CONTROLLER OF NONLINEAR SYSTEMS

A block diagonal form about a nonlinear system is defined. Based on the de finition, a design method ca1led block diagonal controller (BDC) is proPOsed bo feedbacklinearization. Thus, a linearization design of a class of nonlinear system can be simply re-alized. The result of design has been proved by mathematical simulation of a certain anti-ship missile.

Linearizing Control of Induction Motor Based on Networked Control Systems

A new approach to speed control of induction motors is developed by introducing networked control systems （NCSs） into the induction motor driving system. The control strategy is to stabilize and track the rotor speed of the induction motor when the network time delay occurs in the transport medium of network data. First, a feedback linearization method is used to achieve input-output linearization and decoupling control of the induction motor driving system based on rotor flux model, and then the characteristic of network data is analyzed in terms of the inherent network time delay. A networked control model of an induction motor is established. The sufficient condition of asymptotic stability for the networked induction motor driving system is given, and the state feedback controller is obtained by solving the linear matrix inequalities （LMIs）. Simulation results verify the efficiency of the proposed scheme.

Research on Grid-Connected Control Strategy of Distributed Generator Based on Improved Linear Active Disturbance Rejection Control

The virtual synchronous generator(VSG)technology has been proposed to address the problem of system frequency and active power oscillation caused by grid-connected new energy power sources.However,the traditional voltage-current double-closed-loop control used in VSG has the disadvantages of poor disturbance immunity and insufficient dynamic response.In light of the issues above,a virtual synchronous generator voltage outer-loop control strategy based on improved linear autonomous disturbance rejection control(ILADRC)is put forth for consideration.Firstly,an improved first-order linear self-immunity control structure is established for the characteristics of the voltage outer loop;then,the effects of two key control parameters-observer bandwidthω_(0)and controller bandwidthω_(c)on the control system are analyzed,and the key parameters of ILADRC are optimally tuned online using improved gray wolf optimizer-radial basis function(IGWO-RBF)neural network.A simulationmodel is developed using MATLAB to simulate,analyze,and compare the method introduced in this paper.Simulations are performed with the traditional control strategy for comparison,and the results demonstrate that the proposed control method offers superior anti-interference performance.It effectively addresses power and frequency oscillation issues and enhances the stability of the VSG during grid-connected operation.

Robust H_∞ Control for Uncertain Markovian Jump Linear Time-Delay Systems

This paper studies the robust stochastic stabilization and robust H∞ control for linear time-delay systems with both Markovian jump parameters and unknown norm-bounded parameter uncertainties. This problem can be solved on the basis of stochastic Lyapunov approach and linear matrix inequality (LMI) technique. Sufficient conditions for the existence of stochastic stabilization and robust H∞ state feedback controller are presented in terms of a set of solutions of coupled LMIs. Finally, a numerical example is included to demonstrate the practicability of the proposed methods.

Decoupled nonsingular terminal sliding mode control for affine nonlinear systems

A decoupled nonsingular terminal sliding mode control（DNTSMC） approach is proposed to address the tracking control problem of affine nonlinear systems.A nonsingular terminal sliding mode control（NTSMC） method is presented,in which the nonsingular terminal sliding surface is defined as a special nonsingular terminal function and the convergence time of the system states can be specified.The affine nonlinear system is firstly decoupled into linear subsystems via feedback linearization.Then,a nonsingular terminal sliding surface is defined and the NTSMC method is applied to each subsystem separately to ensure the finite time convergence of the closed-loop system.The verification example is given to demonstrate the effectiveness and robustness of the proposed approach.The proposed approach exhibits a considerable advantage in terms of faster tracking error convergence and less chattering compared with the conventional sliding mode control（CSMC）.

Robust H_∞ control for discrete-time polytopic uncertain systems with linear fractional vertices

The robust H∞ control problem for discrete-time uncertain systems is investigated in this paper. The uncertain systems are modelled as a polytopic type with linear fractional uncertainty in the vertices. A new linear matrix inequality (LMI) characterization of the H∞ performance for discrete systems is given by introducing a matrix slack variable which decouples the matrix of a Lyapunov function candidate and the parametric matrices of the system. This feature enables one to derive sufficient conditions for discrete uncertain systems by using parameter-dependent Lyapunov functions with less conservativeness. Based on the result, H∞ performance analysis and controller design are carried out. A numerical example is included to demonstrate the effectiveness of the proposed results.