The problem of the robust D-stability analysis for linear systems with parametric uncertainties is addressed. For matrix polytopes, new conditions via the affine parameter-dependent Lyapunov function of uncertain syst...The problem of the robust D-stability analysis for linear systems with parametric uncertainties is addressed. For matrix polytopes, new conditions via the affine parameter-dependent Lyapunov function of uncertain systems are developed with the benefit of the scalar multi-convex function. To be convenient for applications, such conditions are simplified into new linear matrix inequality （LMI） conditions, which can be solved by the powerful LMI toolbox. Numerical examples are provided to indicate that this new approach is less conservative than previous results for Hurwitz stability, Schur stability and D-stability of uncertain systems under certain circumstances.展开更多
The boundary value problems of the third-order ordinary differential equation have many practical application backgrounds and their some special cases have been studied by many authors. However, few scholars have stud...The boundary value problems of the third-order ordinary differential equation have many practical application backgrounds and their some special cases have been studied by many authors. However, few scholars have studied the boundary value problems of the complete third-order differential equations u′′′(t) = f (t,u(t),u′(t),u′′(t)). In this paper, we discuss the existence and uniqueness of solutions and positive solutions of the fully third-order ordinary differential equation on [0,1] with the boundary condition u(0) = u′(1) = u′′(1) = 0. Under some inequality conditions on nonlinearity f some new existence and uniqueness results of solutions and positive solutions are obtained.展开更多
This note concerns the problem of the robust stability of uncertain neutral systems with time-varying delay and saturating actuators. The system considered is continuous in time with norm bounded parametric uncertaint...This note concerns the problem of the robust stability of uncertain neutral systems with time-varying delay and saturating actuators. The system considered is continuous in time with norm bounded parametric uncertainties. By incorporating the free weighing matrix approach developed recently, some new delay-dependent stability conditions in terms of linear matrix inequalities （LMIs） with some tuning parameters are obtained. An estimate of the domain of attraction of the closed-loop system under a priori designed controller is proposed. The approach is based on a polytopic description of the actuator saturation nonlinearities and the Lyapunov- Krasovskii method. Numerical examples are used to demonstrate the effectiveness of the proposed design method.展开更多
基金supported by the National Natural Science Foundation of China (6090405161021002)
文摘The problem of the robust D-stability analysis for linear systems with parametric uncertainties is addressed. For matrix polytopes, new conditions via the affine parameter-dependent Lyapunov function of uncertain systems are developed with the benefit of the scalar multi-convex function. To be convenient for applications, such conditions are simplified into new linear matrix inequality （LMI） conditions, which can be solved by the powerful LMI toolbox. Numerical examples are provided to indicate that this new approach is less conservative than previous results for Hurwitz stability, Schur stability and D-stability of uncertain systems under certain circumstances.
文摘The boundary value problems of the third-order ordinary differential equation have many practical application backgrounds and their some special cases have been studied by many authors. However, few scholars have studied the boundary value problems of the complete third-order differential equations u′′′(t) = f (t,u(t),u′(t),u′′(t)). In this paper, we discuss the existence and uniqueness of solutions and positive solutions of the fully third-order ordinary differential equation on [0,1] with the boundary condition u(0) = u′(1) = u′′(1) = 0. Under some inequality conditions on nonlinearity f some new existence and uniqueness results of solutions and positive solutions are obtained.
文摘This note concerns the problem of the robust stability of uncertain neutral systems with time-varying delay and saturating actuators. The system considered is continuous in time with norm bounded parametric uncertainties. By incorporating the free weighing matrix approach developed recently, some new delay-dependent stability conditions in terms of linear matrix inequalities （LMIs） with some tuning parameters are obtained. An estimate of the domain of attraction of the closed-loop system under a priori designed controller is proposed. The approach is based on a polytopic description of the actuator saturation nonlinearities and the Lyapunov- Krasovskii method. Numerical examples are used to demonstrate the effectiveness of the proposed design method.
