Exponentially Dissipative Control For Uncertain Impulsive Dynamical Systems

Nowadays, the dissipative control problem of impulsive systems is a hot issue onthe study of control theory. The paper mainly studies the uncertain impulsive system.We emphatically discuss the problem of exponentially dissipative control and exponen-tially passive control for several classes of impulsive systems, whose uncertainties satisfythe norm bounded condition. By constructing Lyapunov functions and using the linearmatrix inequality approach, we ?rstly study exponential dissipativity of the uncertainnonlinear impulsive system, and the su?cient conditions of exponential dissipativity forthis kind of system are given. Then the su?cient conditions of exponential dissipativityfor the closed-loop system because of the state feedback controller are established. Nextwe study exponential dissipativity and performance of H∞ for uncertain linear impulsivesystem, the su?cient conditions of the exponential dissipativity and performance of H∞are established, and the corresponding state feedback controller is designed. A numericalexample to verify its feasibility is given. Finally, we discuss the exponential passivity foruncertain impulsive time-delay systems, the su?cient conditions of exponentially passiveare given for linear and nonlinear impulsive time-delay systems. On this basis, in the statefeedback control, the su?cient conditions of exponential passivity are established. Andthe exponentially passive controllers for linear impulsive time-delay systems are designed.A numerical example is shown to testify the feasibility of the conclusion.