Ee363 Homework 6 Solutions
نویسنده
چکیده
0 = d dt ‖x(t)‖ = 2x(t) ẋ(t) = 2x(t)Ax(t) = x(t) (A+ A )x(t) for all x(t), which occurs if and only A+A = 0, which is the same as A = −A, i.e., A is skew-symmetric. There are many other ways to see this. For example, the norm of the state will be constant provided the velocity vector is always orthogonal to the position vector, i.e., ẋ(t)x(t) = 0. This also leads us to A + A = 0. Another approach uses the state transition matrix e. The system is constant norm provided e is orthogonal for all t ≥ 0. From here, you’d have to argue that A must be skew-symmetric. The system is constant speed if and only if
منابع مشابه
Ee363 Homework 5
pt+1 = αpt + βpt−1 + γpt−2 + wt, yt = pt + vt. Here p is the (scalar) time series we are interested in, and y is the scalar measurement available to us. The process noise w is IID zero mean Gaussian, with variance 1. The sensor noise v is IID Gaussian with zero mean and variance 0.01. Our job is to estimate pt+1, based on knowledge of y0, . . . , yt. We will use the parameter values α = 2.4, β ...
متن کاملEe363 Homework 3 Solutions
1. Solution of a two-point boundary value problem. We consider a linear dynamical system ˙ x = Ax, with x(t) ∈ R n. There is an n-dimensional subspace of solutions of this equation, so to single out one of the trajectories we can impose, roughly speaking, n equations. In the most common situation, we specify x(0) = x 0 , in which case the unique solution is x(t) = e tA x 0. This is called an in...
متن کاملEe363 Homework 8 Solutions
holds for all trajectories of the system, and for all t. Here we interpret u and y as power-conjugate quantities (i.e., quantities whose product gives power) such as voltage and current or force and velocity. The inequality above states that at all times, the total energy delivered to the system since t = 0 is nonnegative, i.e., it is impossible to extract any energy from a passive system. (a) ...
متن کاملEffects of Annotations and Homework on Learning Achievement: An Empirical Study of Scratch Programming Pedagogy
In Taiwan elementary schools, Scratch programming has been taught for more than four years. Previous studies have shown that personal annotations is a useful learning method that improve learning performance. An annotation-based Scratch programming (ASP) system provides for the creation, share, and review of annotations and homework solutions in the interface of Scratch programming. In addition...
متن کامل