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The stability and exact observability problems of discrete stochastic singular systems based on generalised Lyapunov equations are investigated in this study. First, some new conditions for the existence and uniqueness of the solutions to discrete stochastic singular systems are given, and then, a new type generalised Lyapunov equation is proposed. Based on these results, a sufficient condition for...
Scalar feedback control in a chaotic discrete prey predator system is investigated. The existence of the fixed points and the local stability of the positive fixed point are discussed. By using center manifold theorem, it is proved rigorously that the system undergoes the flip bifurcation near the unique positive fixed point. To eliminate the undesirable chaos induced by the flip bifurcation and stabilize...
This paper studies the guaranteed cost control for a class of uncertain switched singular systems based on the guaranteed cost control theories and other related theories about switched systems. Firstly by using the common Lyapunov functions method, a sufficient condition on the existence of state feedback guaranteed cost controller is derived under arbitrary switching laws. Secondly a sufficient...
The robust stability of discrete singular systems with time-varying delay is considered. New delay-dependent stability criteria are proposed, which are dependent on the minimum and maximum delay bounds. A strict delay-dependent linear matrix inequality (LMI) condition is obtained for a discrete singular time-varying system to be regular, causal and stable. The result on robust stability of uncertain...
This paper studies the problem of robust H∞ guaranteed cost control for a class of time-varying uncertain discrete systems with both state and input delays. Suppose that the time-varying uncertain parameters are norm-bounded, but the matched conditions are not required to satisfy. A new sufficient condition of H∞ robust stabilization and satisfies guaranteed cost index is given for the systems by...
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