Implied polynomial matrix equations in multivariable stochastic optimal control

✍ Scribed by K.J. Hunt; M. Šebek

• Publisher: Elsevier Science
• Year: 1991
• Tongue: English
• Weight: 356 KB
• Volume: 27
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/0005-1098(91)90088-j

✦ Synopsis

This paper reports recent work in the theoretical development of the polynomial equation approach to the optimization of multivariable control systems. The algebraic properties of the polynomial matrix equations which define the optimal controller are investigated, and new results concerned with the numerical solvability of the equations are derived.

Notation--All systems considered in this paper are described by means of real polynomial matrices in the delay operator d. The reader is referred to Ku~era (1979) for details. For simplicity the arguments of polynomial matrices are often omitted, such that X(d) is denoted by X. The adjoint of X(d) is written as X*(d)=Xr (d-l). For any polynomial matrix X(d) define (X) as the matrix of terms independent of d. Stable square polynomial matrices are those with zeros of their determinant strictly outside the unit circle of the d-plane. t