Using the Lyapunov function method,this paper investigates the design of state feedback stabilization controllers for fractional order nonlinear systems in triangular form,and presents a number of new results.First,some new properties of Caputo fractional derivative are presented,and a sufficient condition of asymptotical stability for fractional order nonlinear systems is obtained based on the new properties.Then,by introducing appropriate transformations of coordinates,the problem of controller design is converted into the problem of finding some parameters,which can be certainly obtained by solving the Lyapunov equation and relevant matrix inequalities.Finally,based on the Lyapunov function method,state feedback stabilization controllers making the closed-loop system asymptotically stable are explicitly constructed.A simulation example is given to demonstrate the effectiveness of the proposed design procedure.
This paper studies the regional stability for positive switched linear systems with multi-equilibrium points(PSLS-MEP).First, a sufficient condition is presented for the regional stability of PSLS-MEP via a common linear Lyapunov function. Second,by establishing multiple Lyapunov functions, a dwell time based condition is proposed for the regional stability analysis. Third,a suprasphere which contains all equilibrium points is constructed as a stability region of the considered PSLS-MEP, which is less conservative than existing results. Finally, the study of an illustrative example shows that the obtained results are effective in the regional stability analysis of PSLS-MEP.
