By Sergio Bittanti (auth.), Sergio Bittanti, Alan J. Laub, Jan C. Willems (eds.)

Conceived by means of count number Jacopo Francesco Riccati greater than 1 / 4 of a millennium in the past, the Riccati equation has been commonly studied within the next centuries. because its advent up to the mark concept within the sixties, the matrix Riccati equation has recognized a powerful variety of purposes, reminiscent of optimum keep an eye on, H? optimization and powerful stabilization, stochastic attention, synthesis of linear passive networks, to call yet a couple of. This e-book comprises eleven chapters surveying the most thoughts and effects on the topic of the matrix Riccati equation, either in non-stop and discrete time. idea, purposes and numerical algorithms are widely offered in an expository method. As a foreword, the background and prehistory of the Riccati equation is concisely presented.

**Read Online or Download The Riccati Equation PDF**

**Similar nonfiction_8 books**

**Plate Stability by Boundary Element Method**

1. 1 historic heritage skinny plates and shells are primary structural parts in several civil, mechanical, aeronautical and marine engineering layout functions. ground slabs, bridge decks, concrete pavements, sheet pile keeping partitions are all, less than basic lateral loading conditions, circumstances of plate bending in civil engineering.

Good nation fabrics were gaining significance lately in particular within the context of units which may supply worthy infrastructure and adaptability for numerous human endeavours. during this context, microwave fabrics have a special position particularly in quite a few equipment purposes in addition to in conversation networks.

**Molecular Magnetism: From Molecular Assemblies to the Devices**

Molecular Magnetism: From Molecular Assemblies to the units studies the cutting-edge within the zone. it truly is prepared in elements, the 1st of which introduces the elemental suggestions, theories and actual ideas required for the research of the magnetic molecular fabrics, evaluating them with these utilized in the examine of classical magnetic fabrics.

**Controlled Release: A Quantitative Treatment**

The concept that of managed free up has attracted expanding awareness during the last 20 years, with the functions of this know-how proliferating in various fields in cluding drugs, agriculture and biotechnology. study and developmental efforts on the topic of managed liberate are multiplying in either and academia.

- Optical Properties of Narrow-Gap Low-Dimensional Structures
- Emerging Competition in Postal and Delivery Services
- Oxygen Transport to Tissue XI
- Low-Dimensional Electronic Systems: New Concepts
- Bacterial, Phage and Molecular Genetics: An Experimental Course
- Biochemical Differentiation in Insect Glands

**Additional resources for The Riccati Equation**

**Sample text**

45». The following result (proved in [13» describes all minimal unitary completions in terms of hermitian solutions of the associated Riccati equation. 29. 43) t*] is the state characteristic matrix. 44) D* D)I/2; BD*)(1 - DD*)-1/2; Y = (I - D* D)-1/2(iB* H- l - D*C), is a minimal unitary completion ofW(,,\). 43). \) with fixed value at infinity. \). P. Lancaster and L. 11 J-Spectral Factorization Recently, the Hoc optimization problems attracted the attention of many mathematicians and engineers, and the continuous algebraic Riccati equation and its hermitian solutions play a significant role in development of the theory.

49) are necessarily real. 49), and by the maximality property we have X+ ~ X+. This implies X+ = X+, so X+ is real. The same argument applies to X_as well. 4). It is easy to see that X is a real special solution if and only if the graph G(X) (considered as a subspace in R2n) is Mr-invariant and H-nonnegative. 32. Let A, C, D be real with C = C T , D ~ 0 and (A, D) controllable. Assume further that the matrix H is invertible and has signature zero. 49). Proof. 7, we have to demonstrate existence of an n-dimensional Mr-invariant H -non-negative subspace in R2n.

HAUTUS. • Controllability and observability conditions 0/ linear autonomous systems. Ned. Akad. wet. Proc•• Ser. A 12(1969). 443-448. WONHAM. • Linear Multivariable Control, Springer-Verlag. Berlin. 1970 and 1979. RAN. M. and RODMAN. • Stability of invariant maximal semidefinite subspaces II. Applications: selfadjoint rational matrix functions, algebraic Riccati equation. Linear Algebra and Appl. 63(1984). 133-173. PAIGE. C. and VAN LOAN. • A Schur decomposition for Hamiltonian matrices. Linear Algebra and Appl.