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This paper is devoted to the study of a large class of discrete-time backward Riccati equations arising in several linear quadratic (LQ) type control problems both in the deterministic and in the stochastic frameworks. The periodic time-varying case is considered. We propose existence and uniqueness conditions for a global special solution named stabilizing solution for such equations. Beside the stabilizability condition, the criterion derived in this paper is expressed based on some suitable properties of the characteristic multipliers of a discrete-time, periodic linear equation adequately constructed using the coefficients of the given equation. Our result englobes, as particular cases, several existing results in the literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present necessary and sufficient conditions for nonuniform power instability property of linear discrete-time systems in Banach spaces. A characterization of the nonuniform power instability in terms of Lyapunov sequences is also given. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we investigate four concepts of exponential stability for difference equations in Banach spaces. Characterizations of these concepts are given. They can be considered as variants for the discrete-time case of the classical results due to Barbashin and Datko . An illustrative example clarifies the relations between these concepts. [Copyright &y& Elsevier]

This paper focuses on the problem of optimal H 2 filtering for a class of continuous-time stochastic systems without assuming their exponential stability in the mean square sense. Indeed, the stability assumption is relaxed and we assume instead that the Lyapunov operator associated to the dynamical stochastic system is exponentially dichotomic . The optimal solution of the considered optimization problem is expressed in terms of the unique solution of a suitable algebraic Lyapunov equation and the stabilizing solution of a certain algebraic Riccati equation. [ABSTRACT FROM AUTHOR]

Abstract: The aim of this paper is to give some characterizations for weak exponential stability properties of evolution operators in Banach spaces. Variants for weak exponential stability of some well-known results in uniform stability theory (Buşe and Niculescu (2009) , Daleckij and Krein (1974) , Datko (1973) , Rolewicz (1986) , Stoica and Megan (2009) ) are obtained. [ABSTRACT FROM AUTHOR]

This primer article focuses on the representation of solutions and finite-time stability of impulsive first-order delay differential systems. We define delayed matrix function with impulses and use variation of parameters to obtain a representation of solutions of linear systems with impulse effects. The famous classical Grownwall inequalities and properties of delayed matrix exponential with impulses are used to develop sufficient conditions for finite-time stability. In the end, we provide some examples to support the results. [ABSTRACT FROM AUTHOR]