An explicit solution to right factorization with applicationin eigenstructure assignment

Based on the well-known Leverrier algorithm, a simple explicit solution to right factorization of a linear system is established. This solution is expressed by the controllability matrix of the given system and a symmetric operator matrix. Applications of this solution to a type of generalized Sylvester matrix equatiorls and the problem of parametric eigenstructure assignment by state feedback are investigated,and general complete parametric solutions to these two problems are deduced. These new solutions are simple, and possess desirable structural properties which render the solutions readily implementable. An example demonstrates the effect of the proposed results.

Major complications of adult right lobe living liver donors

BACKGROUND：The right lobe of the liver is generally preferred for living donor liver transplantation in adult patients with end-stage liver disease.It is important to know the preoperative factors relating to the major postoperative complications.We therefore evaluated the possible risk factors for predicting postoperative complications in right lobe liver donors.METHODS：Data from 378 donors who had undergone right lobe hepatectomy at our center were evaluated retrospectively. The factors we evaluated induded donor age, gender, body mass index （BMI）, remnant liver volume, operation time, history of previous abdominal surgery, inclusion of the middle hepatic vein and variations in the portal and bile systems. RESUEI＇S： Of the 378 donors, 219 were male and 159 female. None of the donors died, but 124 （32.8%） donors experienced complications including major complications （Clavien scores III and IV） in 27 （7.1%）. Univariate analysis showed that complica- tions were significantly associated with male gender and higher BMI （P〈0.05）, but not with donor age, remnant liver volume, operation time, graft with middle hepatic vein, variations in the portal and bile systems and previous abdominal surgery （P〉0.05）. Multivariate logistic regression analysis showed that major complications were significantly associated with male gender （P=0.005） and higher BMI （P=0.029）. Moreover, the Chi- square test showed that there were significant relationships between major complications and male gender （P=0.010,Z2=6.614, df=l） and BMI 〉25 kg/m2 （P=-0.031, Z2=8.562, df-1）. Of the 96 male donors with BMI 〉25 kg/m2, 14 （14.6%） with major complications had significantly smaller mean remnant liver volume than those （82, 85.4%） without major complications （32.50%± 4.45% vs 34.63%±3.11%, P=0.029）.CONCLUSION： Male donors with BMI 〉25 kg/m2 and a remnant liver volume 〈32.50% had a significantly increased risk for major complications.

Two parametric approaches for eigenstructure assignment in second-order linear systems

This paper considers eigenstructure assignment in second-order linear systems via proportional plus derivative feedback. It is shown that the problem is closely related to a type of so-called second-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two complete parametric methods for the proposed eigenstructure assignment problem are presented. Both methods give simple complete parametric expressions for the feedback gains and the closed-loop eigenvector matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the system, and allows the closed-loop eigenvalues to be set undetermined and sought via certain optimization procedures. An example shows the effectiveness of the proposed approaches. Keywords Second-order linear systems - Eigenstructure assignment - Proportional plus derivative feedback - Parametric solution - Singular value decompoition - Right factorization This work was supported in part by the Chinese Outstanding Youth Foundation (No.69504002).

Closed-form Solutions to the Matrix Equation AX-EXF=BY with F in Companion Form

A closed-form solution to the linear matrix equation AX-EXF = BY with X and Y unknown and matrix F being in a companion form is proposed, and two equivalent forms of this solution are also presented. The results provide great convenience to the computation and analysis of the solutions to this class of equations, and can perform important functions in many analysis and design problems in descriptor system theory. The results proposed here are parallel to and more general than our early work about the linear matrix equation AX-XF = BY .

Unified parametric approaches for high-order integral observer design for matrix second-order linear systems

A type of high-order integral observers for matrix second-order linear systems is proposed on the basis of generalized eigenstructure assignment via unified parametric approaches. Through establishing two general parametric solutions to this type of generalized matrix second-order Sylvester matrix equations, two unified complete parametric methods for the proposed observer design problem are presented. Both methods give simple complete parametric expressions for the observer gain matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the fight factorization of the system, and allows eigenvalues of the error system to be set undetermined and sought via certain optimization procedures. A spring-mass-dashpot system is utilized to illustrate the design procedure and show the effect of the proposed approach.

Operator-Based Robust Nonlinear Control for SISO and MIMO Nonlinear Systems With PI Hysteresis

In this paper, operator based robust nonlinear control for single-input single-output(SISO) and multi-input multi-output(MIMO) nonlinear uncertain systems preceded by generalized Prandtl-Ishlinskii(PI) hysteresis is considered respectively. In detail, by using operator based robust right coprime factorization approach, the control system design structures including feedforward and feedback controllers for both SISO and MIMO nonlinear uncertain systems are given, respectively.In which, the controller design includes the information of PI hysteresis and its inverse, and some sufficient conditions for the controllers in both SISO and MIMO systems should be satisfied are also derived respectively. Based on the proposed conditions, influence from hysteresis is rejected, the systems are robustly stable and output tracking performance can be realized.Finally, the effectiveness of the proposed method is confirmed by numerical simulations.

Operator-Based Robust Nonlinear Free Vibration Control of a Flexible Plate With Unknown Input Nonlinearity

In this paper,a robust nonlinear free vibration control design using an operator based robust right coprime factorization approach is considered for a flexible plate with unknown input nonlinearity.With considering the effect of unknown input nonlinearity from the piezoelectric actuator,operator based controllers are designed to guarantee the robust stability of the nonlinear free vibration control system.Simultaneously,for ensuring the desired tracking performance and reducing the effect of unknown input nonlinearity,operator based tracking compensator and estimation structure are given,respectively.Finally,both simulation and experimental results are shown to verify the effectiveness of the proposed control scheme.

Robust Stability of Nonlinear Plants with a Non-symmetric Prandtl-Ishlinskii Hysteresis Model

In this paper, robust stability of nonlinear plants represented by non-symmetric Prandtl-Ishlinskii （PI） hysteresis model is studied. In general, PI hysteresis model is the weighted superposition of play or stop hysteresis operators, and the slopes of the operators are considered to be the same. In order to make a hysteresis model, a modified form of non-symmetric play hysteresis operator with unknown slopes is given. The hysteresis model is described by a generalized Lipschitz operator term and a bounded parasitic term. Since the generalized Lipschitz operator is unknown, a new condition using robust right coprime factorization is proposed to guarantee robust stability of the controlled plant with the hysteresis nonlinearity. As a result, based on the proposed robust condition, a stabilized plant is obtained. A numerical example is presented to validate the effectiveness of the proposed method.

An Operator-based Nonlinear Vibration Control System Using a Flexible Arm with Shape Memory Alloy

In the past,arms used in the fields of industry and robotics have been designed not to vibrate by increasing their mass and stiffness.The weight of arms has tended to be reduced to improve speed of operation,and decrease the cost of their production.Since the weight saving makes the arms lose their stiffness and therefore vibrate more easily,the vibration suppression control is needed for realizing the above purpose.Incidentally,the use of various smart materials in actuators has grown.In particular,a shape memory alloy(SMA)is applied widely and has several advantages:light weight,large displacement by temperature change,and large force to mass ratio.However,the SMA actuators possess hysteresis nonlinearity between their own temperature and displacement obtained by the temperature.The hysteretic behavior of the SMA actuators affects their control performance.In previous research,an operator-based control system including a hysteresis compensator has been proposed.The vibration of a flexible arm is dealt with as the controlled object;one end of the arm is clamped and the other end is free.The effectiveness of the hysteresis compensator has been confirmed by simulations and experiments.Nevertheless,the feedback signal of the previous designed system has increased exponentially.It is difficult to use the system in the long-term because of the phenomenon.Additionally,the SMA actuator generates and radiates heat because electric current passing through the SMA actuator provides heat,and strain on the SMA actuator is generated.With long-time use of the SMA actuator,the environmental temperature around the SMA actuator varies through radiation of the heat.There exists a risk that the ambient temperature change dealt with as disturbance affects the temperature and strain of the SMA actuator.In this research,a design method of the operator-based control system is proposed considering the long-term use of the system.In the method,the hysteresis characteristics of the SMA actuator and the temperature change around the actuator are considered.The effectiveness of the proposed method is verified by simulations and experiments.