Robust Stability Conditions for Large-Scale Interconnected Systems with Structured and Unstructured Uncertainties

Abstract

The paper is mainly concerned with the problem of decentralized robust stability of large-scale interconnected systems with structured and unstructured uncertainties. A simple method is presented whereby some sufficient conditions are derived so that asymptotic stability of large-scale interconnected systems can be guaranteed in the presence of uncertain perturbations. The method is also extended to large-scale discrete-time systems and the corresponding robust stability conditions are established for uncertain large-scale discrete-time systems. Finally, two numerical examples are given to demonstrate that our robust stability conditions are less conservative than those reported in the control literature.

Robust adaptive decentralized control for a class of networked large-scale systems with sensor network failures

“…Consider the adaptive closed-loop system described by (14) and (13). If there exists a symmetric matrix > 0, and by using the state feedback controller ( ) described in (8) with adaptive laws (10), (11), and control gain function 1 , 2 3 given by (15) and (16). Then one can guarantee that all closed-loop system signals are bounded and the states of systems ( ) converges asymptotically to zero as the time goes to infinity for any ( ) ∈ Δ .…”

“…Thus, for the large scale closed-loop system described by (14), we propose the adaptive robust state feedback controllers (8) with the adaptive laws (10) and (11), and control gain functions 2 and 3 are given by…”

“…Besides, in [9], [10] and [13], adaptive methods are derived for decentralized systems for guaranteeing uniform ultimate boundedness and asymptotic tracking with delayed state perturbations in the communications, respectively. The structured and unstructured uncertainties in decentralized large-scale system are considered in [11] by using eigenvalue assignment method with asymptotic stability results. In [15], the direct adaptive method was proposed to deal with asymptotic fault-tolerant tracking control problem in distributed control systems with actuator and interconnection failures.…”

Robust decentralized stabilization of uncertain large-scale discrete-time systems

“…However, since most of engineering systems are controlled by digital computer, it is important to deal with the problem in discrete time case. Recently, Wu et al (1999) presented a sucient condition for robust stabilization of uncertain large-scale discrete-time systems using matrix norm operation. But a feedback gain matrix has to be preselected in order to check the su cient condition in their method.…”