PPT-On the Stability of Nonlinear Time-Periodic Systems

Haithem E Taha Mechanical and Aerospace Engineering University of California Irvine AEIC 21 22 Mar 2015 Luxor Egypt 2 wake Hovering Insects Hedrick amp Daniel J Exp Biol . 118 brPage 2br Exponential Stability The origin of is exponentially stable if and only if the linearization of at the origin is Hurwitz Theorem Let be a locally Lipschitz function de64257ned over a domain Let be a continuously differentiable functi S Doan A Kalauch and S Siegmund Department of Mathematics Dresden University of Technology 01069 Dresden Germany Received May 19 2008 Revised December 23 2008 Abstract Several notions of exponential stability of linear timeinvariant sys tems on arbit 6 Linearization of Nonlinear Systems In this section we show how to perform linearization of systems described by nonlinear dif ferential equations The procedure introduced is based on the aylor series expansion and It is known as Nyquist stability criterion It is based on the complex analysis result known as Cauchys principle of ar gument Note that the system transfer function is complex function By applying Cauchys principle of ar gument to the openloop syste brPage 1br On the stability of perturbed discrete linear systems with periodic coefficients Abstract KeyWords 1 Introduction nnxnAnx nA nxnnAnx 2 Preliminary results AAA kAmAkm km Imm D Before discussing the stability test let us rst introduce the following notions of stabilit y for a linear time invariant LTI system 1 BIBO stability or zero state stbaility 2 Internal stability or zero input stability Since we have not introduced t consider the follo wing sequences yapuno vlik function Gi en strictly increasing se quence we say is yapuno vlik for if x for 1 is monotone nonincreasing on Switching System Theor em If is yapuno lik for then the switched system is stable Pr oof The S Doan A Kalauch and S Siegmund Department of Mathematics Dresden University of Technology 01069 Dresden Germany Received May 19 2008 Revised December 23 2008 Abstract Several notions of exponential stability of linear timeinvariant sys tems on arbit flow analysis of nonlinear dynamic systems and applications. Jian. Yang. Supervisors: . Dr.. Ye Ping Xiong and Prof. Jing Tang Xing. Faculty . of Engineering and the Environment, University of Southampton, UK. Examples of signals:. Voltage output of a RLC circuit, stock market, ECG, speech, sequences of bases in a gene, MRI or CT scan. Examples of systems:. RLC circuit, an algorithm for predicting future of stock market, an algorithm for detecting abnormal heart rhythms, speech understanding systems, edge detection algorithm for medical images.. Theoretical . and Practical . Challenges. Haithem. E . Taha. Mechanical and Aerospace Engineering. University . of California, Irvine. Cairo University . Aerospace Engineering Department . Tue, Mar 17, 2015. Presented by Glenn Elliott. (with most slides by Jim Anderson and some from Steve Goddard) . Real-Time Basics. Throughout this part of the talk, we assume a . uniprocessor. platform.. 2. A system with a dual notion of correctness:. Stability Analysis of Discrete Time Systems. Mapping Between the s-plane and the z-plane. Mapping Between the s-plane and the z-plane. Mapping Between the s-plane and the z-plane. Mapping Between the s-plane and the z-plane. Dr . Milena . Čukić. Dpt. General Physiology with Biophysics. University of Belgrade, Serbia. Complex dynamics of living systems. Living organisms are complex both in their structures and functions. Parameters of human physiological functions such as arterial blood pressure (.