Lecture 1: Input/Output and State-Space Models This lecture presents some basic definitions and simple examples on nonlinear dynam

3.1.2 A general uniqueness theorem The key issue for uniqueness of solutions turns out to be the maximal slope of a=a(a) to guarantee uniqueness on time interval T=[to, t,, it is sufficient to require existence of a constant M such that

with x(0)=I exist and are unique on the time interval t E [ 0, 1] for allTER\.Then discrete time system(4. 1)with f(5)=r(, i)describes the evolution of continuous time system(4.)at discrete time samples. In particular, if a is continuous then so is f Let us call a point in the closure of X locally attractive for system(4. 1)if there exists

Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.243j(Fall 2003): DYNAMICS OF NONLINEAR SYSTEMS

Proof Existence and uniqueness of r(t, u)and A(t)follow from Theorem 3. 1. Hence, in order to prove differentiability and the formula for the derivative, it is sufficient to show that there exist a function C: R++R+ such that C(r)/r-0 as r-0 and E>0 such

12.1 Systems with controllable linearizations A relatively straightforward case of local controllability analysis is defined by systems with controllable linearizations 12.1.1 Controllability of linearized system Let To: 0, THR, uo: 0, T]H Rm be a

Using control authority to transform nonlinear models into linear ones is one of the most commonly used ideas of practical nonlinear control design. Generally, the trick helps one to recognize \simple\nonlinear feedback design tasks

EROSPACE DYNAMiCS EXAMPLE: GWE ACCELERATIoN of THE TIP 0F认ERU0毛R人TM5Hc人AF LDk小 G For A650LUT # CCELER升T10 N UTH RES/∈ct T0wE工NERT1 AL FRAME (∈ TH IN THiS CASE) 0EFNE兵8uNcH0 f PoINTS

NEWTONs L丹WS ① BoDY CoNTINUES玉 N TTS STATE OF MOT(0N DR REST UNLESS FORCED DI RECTIoNs IMPoRTA

P CDN STANT Wow TAKE THE MOMENT OF MOMENTUM (ANGULAR MOMENTUM) MUST EXPLICITLY DEFINE A POWT ABOUT WHICH WE TAKE THE MOMENT