Bilaterally Flexible Lyapunov Inequalities for Integral Input - to - State Stable Systems
نویسنده
چکیده
This paper investigates stability of interconnection of integral input-to-state stable (iISS) systems. A new tool to verify the stability is proposed by focusing on Lyapunov inequalities each system is to satisfy in accordance with a small-gain-type condition. The purpose of this paper is to extend the technique of “flexible Lyapunov inequalities” developed previously for input-to-state stable(ISS) systems. The achievement is threefold. One is the employment of flexibility for both the systems connected with each other. The former technique only allows the flexibility to appear in one of the mutually connected systems. The second accomplishment is to cover iISS systems. The third is unification of the flexibility in Lyapunov inequalities for iISS and ISS systems. Establishment of the stability is based on explicit construction of C1 Lyapunov functions.
منابع مشابه
Bilaterally Flexible Lyapunov Inequalities for Nonlinear Small-Gain Method Covering iISS Systems
This paper develops a new tool to study stability of interconnection of integral input-to-state stable (iISS) systems. A sort of freedom is introduced into Lyapunov inequalities each system is to satisfy in addition to small-gain-type conditions. The purpose of this paper is to extend the technique of “flexible Lyapunov inequalities” developed previously for input-tostate stable(ISS) systems. T...
متن کاملRobust Adaptive Actuator Failure Compensation of MIMO Systems with Unknown State Delays
In this paper, a robust adaptive actuator failure compensation control scheme is proposed for a class of multi input multi output linear systems with unknown time-varying state delay and in the presence of unknown actuator failures and external disturbance. The adaptive controller structure is designed based on the SPR-Lyapunov approach to achieve the control objective under the specific assump...
متن کاملRobust H_∞ Controller design based on Generalized Dynamic Observer for Uncertain Singular system with Disturbance
This paper presents a robust ∞_H controller design, based on a generalized dynamic observer for uncertain singular systems in the presence of disturbance. The controller guarantees that the closed loop system be admissible. The main advantage of this method is that the uncertainty can be found in the system, the input and the output matrices. Also the generalized dynamic observer is used to est...
متن کاملIntegral Input-to-State Stability for Interconnected Discrete-Time Systems
In this paper, we investigate integral input-to-state stability for interconnected discrete-time systems. The system under consideration contains two subsystems which are connected in a feedback structure. We construct a Lyapunov function for the whole system through the nonlinearly-weighted sum of Lyapunov functions of individual subsystems. We consider two cases in which we assume that one of...
متن کاملExtension of Higher Order Derivatives of Lyapunov Functions in Stability Analysis of Nonlinear Systems
The Lyapunov stability method is the most popular and applicable stability analysis tool of nonlinear dynamic systems. However, there are some bottlenecks in the Lyapunov method, such as need for negative definiteness of the Lyapunov function derivative in the direction of the system’s solutions. In this paper, we develop a new theorem to dispense the need for negative definite-ness of Lyapunov...
متن کامل