On necessity proof of strict bounded real lemma for generalized linear systems with finite discrete jumps

Some preliminary results on strict bounded real lemma for time-varying continuous linear systems are proposed, where uncertainty in initial conditions, terminal cost and extreme of the cost function are dealt with explicitly. Based on these results, a new recursive approach is proposed in the necessity proof of strict bounded real lemma for generalized linear system with finite discrete jumps.

A Certain Subclass of Analytic Functions with Bounded Positive Real Part

For real numbers α and β such that 0≤α<1<β, we denote by T(α,β) the class of normalized analytic functions which satisfy , where U denotes the open unit disk. We find some relationships involving functions in the class T(α,β). And we estimate the bounds of coefficients and solve Fekete-Szego problem for functions in this class. Furthermore, we investigate the bounds of initial coefficients of inverse functions or bi-univalent functions.

H_∞ deconvolution filter design for time-delay linear continuous-time systems

Proposes an H_∞ deconvolution design for time-delay linear continuous-time systems. We first analyze the general structure and innovation structure of the H_∞ deconvolution filter. The deconvolution filter with innovation structure is made up of an output observer and a linear mapping, where the latter reflects the internal connection between the unknown input signal and the output estimate error. Based on the bounded real lemma, a time domain design approach and a sufficient condition for the existence of deconvolution filter are presented. The parameterization of the deconvolution filter can be completed by solving a Riccati equation. The proposed method is useful for the case that does not require statistical information about disturbances. At last, a numerical example is given to demonstrate the performance of the proposed filter.

Bounded Real Lemmas for Fractional Order Systems

This paper derives the bounded real lemmas corresponding to L∞norm and H∞norm(L-BR and H-BR) of fractional order systems. The lemmas reduce the original computations of norms into linear matrix inequality(LMI) problems, which can be performed in a computationally efficient fashion. This convex relaxation is enlightened from the generalized Kalman-YakubovichPopov(KYP) lemma and brings no conservatism to the L-BR. Meanwhile, an H-BR is developed similarly but with some conservatism.However, it can test the system stability automatically in addition to the norm computation, which is of fundamental importance for system analysis. From this advantage, we further address the synthesis problem of H∞control for fractional order systems in the form of LMI. Three illustrative examples are given to show the effectiveness of our methods.

Some Radius Problems Related to a Certain Subclass of Analytic Functions

For real parameters αand β such that 0≤α 〈 1 〈β, we denote by S（α,β） the class of normalized analytic functions which satisfy the following two-sided inequality：where U denotes the open unit disk. We find a sufficient condition for functions to be in the class S（α,β） and solve several radius problems related to other well-known function classes.

H_(2)/H_(∞) Control for Stochastic Jump-Diffusion Systems with Markovian Switching

In this paper, a stochastic H2/H∞ control problem is investigated for Poisson jumpdiffusion systems with Markovian switching, which are driven by a Brownian motion and a Poisson random measure with the system parameters modulated by a continuous-time finite-state Markov chain.A stochastic jump bounded real lemma is proved, which reveals that the norm of the perturbation operator below a given threshold is equivalent to the existence of a global solution to a parameterized system of Riccati type differential equations. This result enables the authors to obtain sufficient and necessary conditions for the existence of H2/H∞ control in terms of two sets of interconnected systems of Riccati type differential equations.