A general invariance principle for nonlinear time-varying systems and its applications

A general invariance principle is proposed from the output-to-state viewpoint for a class of nonlinear time-varying systems. This is achieved by the construction of a simple and intuitive criterion using integral inequality involving the output function and modified detectability conditions. The well-known “LaSalle invariance principle” is shown to be deduced from the proposed approach when a Lyapunov function is given to the applied systems. A similar criterion, the so-called “integral invariance principle”, was proposed by Byrnes and Martin (1995) for nonlinear time-invariant systems. However, in general, these two approaches cannot be applied to time-varying systems directly. The proposed scheme can be viewed as an extension of the integral invariance principle for time-invariant systems to time-varying systems. Such extension is non-trivial and can be used in various research areas, such as adaptive control, tracking control and the control of driftless systems. Applications to the global tracking control of four-wheeled mobile robots are given to demonstrate the feasibility and validity of the proposed approach