Finite-time Stability Analysis And Synthesis For Linear Time-delay Systems

Finite-time stability can better describe the transient behavior of a system over a cer-tain time interval than the traditional asymptotic stability. A system is said to be finite-time stable if, given a bound on the initial condition, its state does not exit a certain domain dur-ing a specified time interval. Therefore, for systems that are known to operate only over a short time interval or whenever, from practical considerations, the system state is required to remain within a prescribed bound, finite-time stability (FTS) can be used.On the basis of the FTS-related concepts, by employing the Lyapunov-like function method or the delay differential inequality method, FTS analysis and synthesis problems are discussed for linear time-delay systems, linear discrete singular time-delay systems and linear impulsive switched time-delay systems. Then, the obtained FTS-related results are further applied to linear networked control systems and linear structural systems for controller design issues. The main contributions are summarized as follows:·The problems of FTS analysis and synthesis are investigated for linear discrete sys-tems with time-varying delay. Correspondingly, the problems of input-output finite-time stability (IO-FTS) analysis and synthesis are studied for linear continuous systems with time-invariant delay. Some pertinent conditions are obtained based on the Lyapunov-like function method. Numerical examples are provided to illustrate the validity of the obtained results.·A new FTS concept, which is defined as admissible finite-time stability (AFTS), is introduced into discrete singular systems. The problems of AFTS analysis and synthesis are addressed for two types of uncertain discrete singular systems (that is, without delay or with time-varying delay), respectively. By using the Lyapunov-like function method, sufficient conditions are proposed for the AFTS of the concerned two uncertain singular systems. Based on the AFTS analysis results, robust state-feedback controllers are designed respectively such that the correspondingly closed-loop systems are admissible finite-time stable for all admissible uncertainties.·The FTS analysis problem is considered for a class of linear impulsive switched sys-tems with time-varying delay. The DDI method, rather than the commonly used Lyapunov-like function method, is employed to establish a sufficient condition for the system to be finite-time stable. This condition can be expressed in terms of some algebraic inequalities. Compared with the Lyapunov-like function method, the FTS conditions based on the DDI method are easier for checking and do not require FTS of each subsystem.·The obtained FTS-related results on linear time-delay systems are applied to net-worked control systems (NCSs) and structural systems for controller design issues. For the NCS, a mixed controller design method, which guarantees the asymptotic stability of the closed-loop system in the usual case and the FTS of the closed-loop system in the un-usual case (that is, in some particular time intervals, large network-induced delay or packet dropout occurs), is presented. For the structural system with input delay, the controller is designed by taking account of both asymptotic stability and IO-FTS, which can result in limited amplitudes of some variables. For the above two types of systems, some sim-ulation examples are given respectively to demonstrate the effectiveness of the designed controllers.