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

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.

Robust Strictly Positive Real Synthesis for Polynomial Families of Arbitrary Order

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.

Robust SPR Synthesis for Low-Order Polynomial Segments and Interval Polynomials

We prove that, for low-order (n < 5) stable polynomial segments or interval polynomials, there always exists a fixed polynomial such that their ratio is SPR-invariant, thereby providing a rigorous proof of Anderson's claim on SPR synthesis for the fourth-order stable interval polynomials. Moreover, the relationship between SPR synthesis for low-order polynomial segments and SPR synthesis for low-order interval polynomials is also discussed.

Output Feedback Controller Synthesis for Negative Imaginary Systems

This paper presents necessary and sufficient conditions for deriving a strictly proper dynamic controller which satisfies the negative imaginary output feedback control problem. Our synthesis method divides the output feedback control problem into a state feedback problem and a dual output injection problem. Thus, a controller is formed using the solutions to a pair of dual algebraic Riccati equations. Finally, an illustrative example is offered to show how this method may be applied.

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。