Necessary and sufficient stability condition for second-order switched systems: a phase function approach

Necessary and sufficient condition for stabilizability of discrete-time linear switched systems: A set-theory approach

In this paper, the stabilizability of discrete-time linear switched systems is considered. Several sufficient conditions for stabilizability are proposed in the literature, but not a necessary and sufficient one. The main contribution is a computation-oriented necessary and sufficient condition for stabilizability based on set-theory. Based on such a condition, an algorithm for computing the Ly...

Necessary and Sufficient Stability Condition of Discrete State Delay Systems

Abstract: A new method to solve a Lyapunov equation for a discrete delay system is proposed. Using this method, a Lyapunov equation can be solved from a simple linear equation and N -th power of a constant matrix, where N is the state delay. Combining a Lyapunov equation and frequency domain stability, a new stability condition is proposed for a discrete state delay system whose state delay is ...

Necessary and sufficient conditions for absolute stability: the case of second-order systems

Necessary and sufficient stability condition of fractional-order interval linear systems

Keywords: Fractional-order linear systems Interval uncertainty Necessary and sufficient stability condition a b s t r a c t This paper establishes a necessary and sufficient stability condition of fractional-order interval linear systems. It is supposed that the system matrix A is an interval uncertain matrix and fractional commensurate order belongs to 1 ≤ α < 2. Using the existence condition ...

Necessary and Sufficient Condition for Stability of Generalized Expectation Value

Given a probability distribution {pi}i 1,2,...,W , that is, 0 ≤ pi ≤ 1 i 1, 2, . . . ,W and ∑W i 1 pi 1, the ordinary expectation value of a quantity Q of a system under consideration is defined by ∑W i 1 piQi, where W is the total number of accessible states and is enormously large in statistical mechanics, typically being 210 23 . In the field of generalized statistical mechanics for complex ...