Polynomial Bounds for Decoupling, with Applications
نویسندگان
چکیده
Let f(x) = f(x1, . . . , xn) = ∑ |S|≤k aS ∏ i∈S xi be an n-variate real multilinear polynomial of degree at most k, where S ⊆ [n] = {1, 2, . . . , n}. For its one-block decoupled version,
منابع مشابه
Decomposing Overcomplete 3rd Order Tensors using Sum-of-Squares Algorithms
Tensor rank and low-rank tensor decompositions have many applications in learning and complexity theory. Most known algorithms use unfoldings of tensors and can only handle rank up to nbp/2c for a p-th order tensor in Rnp . Previously no efficient algorithm can decompose 3rd order tensors when the rank is super-linear in the dimension. Using ideas from sum-of-squares hierarchy, we give the firs...
متن کاملDecoupling of descriptor systems - Control Theory and Applications [see also IEE Proceedings-Control Theory and Applications], IEE Pr
Using the descriptor standard form, the decoupling problem of the descriptor system by state feedback is studied. The descriptor system is first transformed in controller form and the necessary and sufficient conditions for the descriptor system to be integrator decoupled are obtained. Then, these conditions are shown to be necessary and sufficient for the closed-loop system poles to be assigne...
متن کاملAdaptive Control of Three – Tank – System Using Polynomial Methods
Adaptive control of a three – tank system laboratory model is presented. The objective laboratory model is a two input – two output (TITO) nonlinear system. It is based on experience with authentic industrial control applications. Two control algorithms utilizing polynomial theory and pole – placement were applied and compared. The first one is based on the traditional 1DOF (one – degree of fre...
متن کاملPerturbation Bounds for Determinants and Characteristic Polynomials
We derive absolute perturbation bounds for the coefficients of the characteristic polynomial of a n × n complex matrix. The bounds consist of elementary symmetric functions of singular values, and suggest that coefficients of normal matrices are better conditioned with regard to absolute perturbations than those of general matrices. When the matrix is Hermitian positivedefinite, the bounds can ...
متن کاملEnvironment for CAD and verification of self-tuning controllers
The contribution deals with an adaptive controllers’ library designed under MATLAB – Simulink environment. The library enables design and verification of two input – two output (TITO) discrete self – tuning controllers. It is a completely open system based on Simulink features. Design of the TITO controllers that are included into the library is based on polynomial methods. The controllers are ...
متن کامل