Stability in terms of two measures for nonlinear impulsive systems on time scales by comparison method. (English) Zbl 1263.93177

Zhang, Kexue; Liu, Xinzhi

Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 19, No. 2, 145-176 (2012).

Summary: This paper studies stability problem in terms of two measures for a class of nonlinear impulsive systems on time scales. By establishing a new comparison result, we derive several stability criteria in terms of two measures for nonlinear impulsive systems on time scales. As applications, nonlinear impulsive control problems of continuous and discrete chaotic systems are discussed. Some less conservative nonlinear impulsive stabilization criteria are obtained where both nonuniform and uniform impulsive intervals are considered. Four examples are discussed to illustrate the effectiveness of our results and the proposed impulsive control schemes.

MSC:

93D05	Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C70	Time-scale analysis and singular perturbations in control/observation systems
93C10	Nonlinear systems in control theory
34H10	Chaos control for problems involving ordinary differential equations

Keywords:

stability in terms of two measures; impulsive systems; time scales; impulsive control; chaotic systems