New Criterion of Robust Hܣ Stabilization for Uncertain Neutral Systems

The problems of delay-dependent robust stability and stabilization for a class of uncertain neutral systems are investigated in this paper. At first, by constructing a new Lyapunov functional and using the Lyapunov stability theory, a new delay-dependent condition which renders the system with no external disturbance and input to be asymptotically stable is obtained and given by a linear matrix inequality. Then, based on the obtained condition, a state feedback stabilize law is designed, which guarantees closed-loop neutral systems are asymptotically stable for all the permitted uncertainties when the external disturbance is naught, and it can also guarantee the closed-loop systems have performance under the external disturbance. The model of neutral systems with both the uncertainty and the disturbance discussed in this paper has rarely been considered before.

M-Matrix-Based Robust Stability and Stabilization Criteria for Uncertain Switched Nonlinear Systems with Multiple Time-Varying Delays

This paper focuses on the robust stability and the memory feedback stabilization problems for a class of uncertain switched nonlinear systems with multiple time-varying delays. Especially, the considered time delays depend on the subsystem number. Based on a novel common Lyapunov functional, the aggregation techniques, and the Borne and Gentina criterion, new sufficient robust stability and stabilization conditions under arbitrary switching are established. Compared with existing results, the proposed criteria are explicit, simple to use, and obtained without finding a common Lyapunov function for all subsystems through linear matrix inequalities, considered very difficult in this situation. Moreover, compared with the memoryless one, the developed controller guarantees the robust stability of the corresponding closed-loop system with more performance by minimizing the effect of the delays in the system dynamics. Finally, two numerical simulation examples are shown to prove the practical utility and the effectiveness of the proposed theories.