@article{d1b357c35db5440284bcf8c935b42bef,

title = "Inversion of Separable Kernel Operators in Coupled Differential-Functional Equations and Application to Controller Synthesis",

abstract = "This article presents the inverse of the kernel operator associated with the complete quadratic Lyapunov-Krasovskii functional for coupled differential-functional equations when the kernel operator is separable. Similar to the case of time-delay systems of retarded type, the inverse operator is instrumental in control synthesis. Unlike the power series expansion approach used in the previous literature, a direct algebraic method is used here. It is shown that the domain of definition of the infinitesimal generator is an invariant subspace of the inverse operator if it is an invariant subspace of the kernel operator. The process of control synthesis using the inverse operator is described, and a numerical example is presented using the sum-of-square formulation.",

keywords = "Lyapunov-Krasovskii functional, linear operator, sum-of-squares, time delay",

author = "Guoying Miao and Matthew Peet and Keqin Gu",

note = "Funding Information: ⋆ D ∈ R , and r > 0 is tifle delay, R and R denote This work was supported by National Natural Science Foundation the set of real vectors and flatrices with m×n diflensions, Funding Information: ⋆ This work was supported by National Natural Science Foundation the set of real vectors and flatrices with m×n diflensions, of⋆ TPhRisCwhoirnkawuansdseurpGproarntetd6b1y37N40a9ti0o,n6a1l5N0a3t1u8r9a,ltShceieNncaetuFroaulnSdcaietniocne respectivelyΞ The initial conditions are defined as This work was supported by National Natural Science Foundation respectivelyΞ The initial conditions are defined as Funding Information: FwoausnadlsaotiosunpopfoJritaendgsbuyPNrSovFinGcreaunntsde1r5G38r3a7n4t,B1K30210616500,92163.0T18h5i1s work x(y00) = φψ ∈ PRCn(r, m), Foundation of Jiangsu Province under Grant BK20150926. This work x(00) = ψ ∈ R Funding Information: was also supported by NSF Grants 1538374, 1301660, 1301851 y0 = φ ∈ PC(r,m), was also supported by NSF Grants 1538374, 1301660, 1301851 y0 = φ ∈ PC(r,m),",

year = "2017",

month = jul,

doi = "10.1016/j.ifacol.2017.08.595",

language = "English (US)",

volume = "50",

pages = "6513--6518",

journal = "IFAC-PapersOnLine",

issn = "2405-8963",

publisher = "IFAC Secretariat",

number = "1",

}