Stability analysis for a kind of multi-variable linear systems with delayed state

Some sufficient conditions for exponential stability of linear neutral functional differential equations

This paper focuses on a class of stochastic differential equations with mixed delay based on Lyapunov stability theory, Itô formula, stochastic analysis, and inequality technique. A sufficient condition for existence and uniqueness of the adapted solution to such systems is established by employing fixed point theorem. Some sufficient conditions of exponential stability and corollaries for such systems are obtained by using Lyapunov function. By utilizing Doob’s martingale inequality and Borel-Cantelli lemma, it is shown that the exponentially stable in the mean square of such systems implies the almost surely exponentially stable. In particular, our theoretical results show that if stochastic differential equation is exponentially stable and the time delay is sufficiently small, then the corresponding stochastic differential equation with mixed delay will remain exponentially stable. Moreover, time delay upper limit is solved by using our theoretical results when the system is exponentially stable, and they are more easily verified and applied in practice.

Stability analysis of 2D Roesser systems via vector Lyapunov functions

Exponential stability of discrete-time systems, stability domains, and state bounds are obtained with the use of vector norm Lyapunov functions. For linear systems, necessary and sufficient conditions are given for asymptotic stability, and exponential bounds are derived. For nonlinear systems, sufficient conditions for exponential stability also yield a stability domain and exponential bounds. Applications are demonstrated in observer design for uncertain discrete-time nonlinear systems. >

In this paper, the exponential stability analysis for ODE switched systems with time delay is extended to distributed parameter switched systems (DPSS) in Hilbert space. For a given family of exponential stable subsystems, this paper focuses on finding conditions to guarantee the overall DPSS’ exponential stability. Based on semigroup theory, by applying piecewise Lyapunov-Krasovskii functionals method incorporated average dwell time approach, sufficient conditions for exponential stability are derived. These conditions are given in the form of linear operator inequalities (LOIs) where the decision variables are operators in Hilbert space, and the stability properties depend on switching rule. Being applied to heat switched propagation equations, these LOIs are reduced to standard Linear Matrix Inequalities (LMIs). Finally, a numerical example is given to illustrate the effectiveness of the proposed result.

A novel approach to the design of decentralized controllers for large-scale systems by dynamic/static output state feedback is presented. A new formulation of the interaction which introduces some degrees of freedom into the design procedure is offered. Sufficient conditions for exponential stability with desirable rate of decay and maximal robustness to unstructured uncertainties in the controller and plant parameters are established. The derived conditions are generic, applicable to nonsquare and nonminimum-phase systems, and independent of the number of system states, inputs and outputs. Based on minimal sensitivity design of isolated subsystems, an analytical method for the satisfaction of the aforementioned sufficient conditions is presented. To this end, through eigenstructure assignment, compact-form sufficient conditions for minimal sensitivity are derived. Illustrative examples are presented to demonstrate the effectiveness of the proposed methodology. Genetic algorithm is employed in th...

2021 Benjamin Franklin Medal in Mechanical Engineering presented to C. Daniel Mote, Jr., Ph.D.

Lyapunov stability analysis for nonlinear systems with state-dependent state delay

This article explores the exponential stabilization issue of a class of state-based switched inertial complex-valued neural networks with multiple delays via event-triggered control. First, the state-based switched inertial complex-valued neural networks with multiple delays are modeled. Second, by separating the real and imaginary parts of complex values, the state-based switched inertial complex-valued neural networks are transformed into two state-based switched inertial real-valued neural networks. Through the variable substitution method, the model of the second-order inertial neural networks is transformed into a model of the first-order neural networks. Third, an event-triggered controller with the transmission sequence is designed to study the exponential stabilization issue of neural networks constructed above. Then, by constructing the Lyapunov functions and based on some inequalities, we obtain sufficient conditions for exponential stabilization of the proposed neural networks. Furthermore, it is proved that the Zeno phenomenon cannot happen under the designed event-triggered controller. Finally, a simulation example is given to illustrate the correctness of the results.

This study examines neural network systems exponential stability, a critical characteristic that guarantees the bounded ness and long-term convergence of network states. Using Linear matrix inequality and Lyapunov functional methods, we prove sufficient conditions for exponential stability. The system's state trajectory converges exponentially to an equilibrium point under suitable conditions, as demonstrated by the stability criteria derived from the network's weight matrices, activation functions, and time delays. Our results are validated by theoretical proofs and numerical simulations, showing the usefulness of the findings for control systems, computational neuroscience, and deep learning architectures.

International audience

Exponential stability and periodicity of impulsive cellular neural networks with time delays

A graph-theoretic approach to exponential stability of stochastic complex networks with time-varying delays

Stability and [formula omitted]-gain analysis for switched delay systems: A delay-dependent method

This technical note is concerned with exponential stability analysis of linear time-varying systems represented by the second-order vector differential equations with the singular leading coefficient matrix. Using bounding techniques on the trajectories of the linear time-varying systems, the stability problem of the time-varying systems is transformed to that of the time-invariant systems and a new sufficient condition for exponential stability is derived. The obtained condition can be applied to the nonsingular case and it is proven that the condition for the nonsingular case is superior to a test presented in the recent literature. Analogously, the proposed method is also extended to the stability analysis for a class of linear time-varying systems with delay. By illustrative examples, better results are obtained by the proposed criteria as compared with some results in the literature.