Relativized collapsing between BPP and PH under stringent oracle access

We propose a new model of stringent oracle access defined for a general complexity class. For example, when comparing the power of two machine models relative to some oracle set X, we restrict that machines of both types ask queries from the same segment of the set X. In particular, for investigating polynomial-time (or polynomial-size) computability, we propose polynomial stringency, bounding query length to any fixed polynomial of input length. Under such stringent oracle access, we show an oracle G such that BPP^G = PH^G.     

Simplified adaptive control via improved robust positive real conditions

A new method is derived for embedding plants in a robust state-feedback scheme, to achieve strictly positive realness of the resulting augmented plants. A state-feedback gain is derived that guarantees the strictly positive realness of the closed-loop in presence of polytopic type, possibly time-varying, parameter uncertainties in the model that describes the plant. This is achieved by assigning different Lyapunov functions to each of the vertices of the uncertainty polytope. The obtained feedback gain is used to apply existing methods for robust simplified adaptive control on systems with possibly time-varying polytopic uncertainties.     

一般线性系统的Farkas引理

为了将仅针对特殊线性系统的Farkas引理推广到一般线性系统，本文利用择一定理给出了一般线性系统的Farkas引理，并由此推导出常用线性系统的Farkas引理，所得结果简明通用。     

基于LMI的不确定组合大系统的分散鲁棒H∞控制

根据有界实引理,研究不确定组合大系统的分散鲁棒H∞控制问题.应用线性矩阵不等式的方法,给出了系统可分散鲁棒镇定且具有H∞性能γ的充要条件,通过建立和求解一个凸优化问题,提出了最优H∞控制律设计方法,并用实例验证了所得结论的正确性.     

On the Barbalat lemma extension for the generalized conformable fractional integrals: Application to adaptive observer design

The Barbalat-type lemma for the generalized conformable fractional-order derivative is examined in this work. An adaptive observer design is presented as an application to validate such proposed theory.     

Finite-frequency output feedback MPC for Markov jump systems

This paper investigates a general design framework of dynamic output feedback model predictive control (DOFMPC) for Markov jump systems within both time and frequency domain. Such a design with guaranteed H_∞ and quadratic performance is formulated by a standard semi-definite programming (SDP), and it is achieved by employing a special congruence transformation. The SDP condition greatly reduces the computational effort by eliminating bilinear matrix inequalities or equation constraints reported in existing references. Specifically, the H_∞ norm of the transfer function is optimized within three types of frequency ranges on account of generalized Kalman–Yakubovic–Popov (GKYP) lemma. The quadratic index is optimized online via SDP. Finally, we verify the feasibility and effectiveness of the proposed method from both theoretical and practical point of view.     

H∞ filtering for continuous fractional-order 2D Roesser model: The 0<α≤1 case

This paper investigates the $H_{\infty }$ filtering for the continuous fractional-order (FO) two-dimensional (2D) Roesser model with the FO between 0 and 1. Firstly, a sufficient condition to ensure the stability and bounded realness in the sense of $H_{\infty }$-norm for the continuous FO 2D Roesser model is given in the form of linear matrix inequalities (LMIs). Secondly, based on the bounded real lemmas proposed above, the $H_{\infty }$ filtering problem for continuous FO 2D Roesser model is addressed through some congruent transformation and matrix transformation. The results are given in LMI form, and the parameters of the continuous FO 2D filters can be achieved from the LMIs easily. In the end, the effectiveness of the proposed results is verified by two numerical examples.     

一般的基于身份签名体制与Forking引理

密码体制的安全性评估是密码体制设计中非常关键的环节,基于计算复杂度的可证安全理论是当前获取安全性证据的一个有效途径。文章首先将一般签名体制的概念直接扩展,得到一般的基于身份签名体制的概念,并证明了这类体制上的Forking引理,由此提供了一种在随机谕示模型下,利用扩展的Forking引理证明一般的基于身份签名体制安全性的途径。以Hess体制为例,给出了该体制的安全性证明。