Robust Strictly Positive Real Synthesis for Polynomial Families of Arbitrary Order

Robust Strictly Positive Real Synthesis for Convex Combination of Sixth-Order Polynomials

For the two sixth-order polynomials $a(s)$ and $b(s),$ Hurwitz stability of their convex combination is necessary and sufficient for the existence of a polynomial $c(s)$ such that $c(s)/a(s)$ and $c(s)/b(s)$ are both strictly positive real. Our reasoning method is constructive, and is insightful and helpful in solving the general robust strictly positive real synthesis problem.

Complete Solution to the General Robust Strictly Positive Real Synthesis Problem for Polynomial Segments

For any two n-th order polynomials a(s) and b(s), the Hurwitz stability of their convex combination is necessary and sufficient for the existence of a polynomial c(s) such that c(s)/a(s) and c(s)/b(s) are both strictly positive real.

Geometric Characterization of Strictly Positive Real Regions and its Applications

Strict positive realness (SPR) is an important concept in absolute stability theory, adaptive control, system identification, etc. This paper characterizes the strictly positive real regions in coefficient space and presents a robust design method for SPR transfer functions. We first introduce the concepts of SPR regions and weak SPR regions and show that the SPR region associated with a fixed polynomial is unbounded, whereas the weak SPR region is bounded. We then prove that the intersection of several weak SPR regions associated with different polynomials can not be a single point. Furthermo…

On the achievable degree of stability in strictly negative imaginary state feedback control

In this paper we study the problem of determining the largest degree of stability that can be achieved for SISO systems using negative imaginary state feedback control. A state feedback result is given for synthesising a controller for a plant such that a given closed-loop transfer function is strictly negative imaginary with a prescribed degree of stability. By varying a parameter, the placement of the closed-loop system poles can be adjusted to give a prescribed degree of stability. We show the achievable degree of stability is related to the zero locations of the transfer function from the …

社交网络上闭环推荐系统的结构化正定最优控制综合

Structured Positive-Definite Optimal Control Synthesis of Closed-Loop Recommendation Systems over Social Networks

本研究将社交网络多主题意见动态的推荐策略设计建模为无限时域线性二次最优控制问题，通过结构化正定控制器综合实现性能与局部性的权衡，并给出数值验证。

Negative Imaginary State Feedback Control with a Prescribed Degree of Stability

This paper presents a method for the synthesis of negative imaginary closed-loop systems with a prescribed degree of stability under the assumption of full state feedback. The approach extends existing work by using a perturbation method to ensure a closed-loop system that has both the negative imaginary property and a prescribed degree of stability. This approach involves the real Schur decomposition of a matrix followed by the solution to two Lyapunov equations which provides computational advantages over alternate state feedback synthesis techniques. Also, some counterexamples are presented…