Stability of moving invariant sets and uncertain dynamic systems on time scales
- Florida Tech., Melbourne, FL (United States)
- Embry-Riddle Aeronautical Univ., Daytona Beach, FL (United States)
Nonlinear differential equations with uncertain parameters may cause change of equilibrium-states. To investigate such situations, Siljak, Ikeda and Ohata have introduced the notion of parametric stability and discussed its study which is interesting in itself. A fundamental feedback control problem is that of obtaining some desired behavior from the given system which has uncertain information. Leitmann and associates have dealt with such a problem in a series of papers. They have investigated continuous and discrete uncertain systems by means of Lyapunov functions. Recently, a theory known as dynamic systems on time scales has been built which incorporates both continuous and discrete times, namely, time as an arbitrary closed sets of reals, and permit us to handle both systems simultaneously. This theory allows one to get some insight into and better understanding of the subtle differences between discrete and continuous systems. To study uncertain systems, a different idea is employed in, which exhibits moving invariant sets as the parameter changes. By reducing the problem to a simpler comparison problem, the stability of moving invariant sets is discussed employing comparison method. The derivative of the Lyapunov function involved is estimated from opposite directions relative to suitable sets in phase space that depend on the moving parameter. In this paper, utilizing the framework of the theory of dynamic systems on time scale, we shall investigate uncertain dynamic systems on time scale relative to stability of moving invariant sets. As an application of our results, we shall consider the control of uncertain dynamic system on time scales and obtain the desired stability behavior of moving invariant sets. For some preliminary work in this direction see.
- OSTI ID:
- 482012
- Report Number(s):
- CONF-960503-; TRN: 97:002904-0044
- Resource Relation:
- Conference: 1. international conference on nonlinear problems in aviation and aerospace, Daytona Beach, FL (United States), 9-11 May 1996; Other Information: PBD: 1994; Related Information: Is Part Of First international conference on nonlinear problems in aviation & aerospace; Sivasundaram, S. [ed.]; PB: 729 p.
- Country of Publication:
- United States
- Language:
- English
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