This paper presents the design of an additive fault tolerant control for nonlinear time-invariant singularly perturbed systems against actuator faults based on Lyapunov redesign principle. The overall system is reduced into subsystems with fast and slow dynamic behavior using singular perturbation method. The time scale reduction is carried out when the singular perturbation parameter is set to...

The notion of incremental stability was proposed by several researchers as a strong property of dynamical and control systems. In this type of stability, trajectories converge to each other, rather than to an equilibrium point or a particular trajectory. Similarly to stability, Lyapunov functions play an important role in the study of incremental stability. In this paper, we propose coordinate-...

In this paper we present singularly impulsive or generalized impulsive dynamical systems. Dynamics of this system is characterized by the set of differential, difference, and algebraic equations. They represent the class of hybrid systems, where algebraic equations represent constraints that differential and difference equations need to satisfy. Generalized term have as source generalized syste...

Based on the theory of calculus on time scales, the homeomorphism theory, Lyapunov functional method, and some analysis techniques, sufficient conditions are obtained for the existence, uniqueness, and global exponential stability of the equilibrium point of Cohen-Grossberg bidirectional associative memory BAM neural networks with distributed delays and impulses on time scales. This is the firs...

In this paper, we propose new LMI-based conditions for robust stability/performance analysis of linear timeinvariant (LTI) uncertain systems. To get around the conservatism of existing conditions resulting from Lyapunov’s stability theory, we first consider to employ Lyapunov functions that can be associated with higher-order derivatives of the state vectors. This motivates us to introduce a re...

Stability analysis of polynomial differential equations is a central topic in nonlinear dynamics and control which in recent years has undergone major algorithmic developments due to advances in optimization theory. Notably, the last decade has seen a widespread interest in the use of sum of squares (sos) based semidefinite programs that can automatically find polynomial Lyapunov functions and ...

Many processes in automatic regulation, physics, mechanics, biology, economy, ecology etc. can be modelled by hereditary equations (see, e.g. [1±6]). One of the main problems for the theory of stochastic hereditary equations and their applications is connected with stability. Many stability results were obtained by the construction of appropriate Lyapunov functionals. In [7± 11], the procedure ...