Abstract
This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs) and linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed methodology.
Highlights
Most practical systems, such as missile systems and satellite systems, possess a typical characterization that their operating times always have a finite duration
This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps
The main concern for the researchers is the stability over a fixed finitetime interval rather than the classical Lyapunov asymptotic stability, the Lyapunov theory is pervasive in control fields from linear methods to nonlinear systems
Summary
Most practical systems, such as missile systems and satellite systems, possess a typical characterization that their operating times always have a finite duration In this case, the main concern for the researchers is the stability over a fixed finitetime interval rather than the classical Lyapunov asymptotic stability, the Lyapunov theory is pervasive in control fields from linear methods to nonlinear systems. In [7], the problem of finite-time stabilization for linear systems via jump control is researched through Lyapunov functions. In [8], FTS for time-varying linear systems with jumps is discussed, where a necessary and sufficient condition was obtained. Note that this condition is difficult to test. A sufficient condition involving two coupled differential-difference linear matrix inequalities for FTS is presented in [8], which is much easier to be handled
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