J. Sreedhar and P. Van Dooren. Periodic Schur form and some matrix equations. In U. Helmke, R. Mennicken, and J. Saurer, editors, Proc. MTNS'93, Regensburg, Germany, volume I, pages 339--362, 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....models which are the primary mathematical descriptions encountered in several practical applications. In the last few years there has been a constantly increasing interest for the development of numerical algorithms for the analysis and design of linear periodic discrete time control systems [1, 2, 3]. In this paper we discuss the numerical solution of the optimal periodic output feedback LQG control problem by using a gradient search based optimization approach. For the evaluation of the cost function and its gradient explicit expressions are derived which involve the numerical solution of a ....

....because of a much higher computational effort involved in solving a single periodic Lyapunov equation. This goal can be achieved with the algorithms proposed in the next section. 3. Solution of DPLEs Several possible computational approaches to solve periodic Lyapunov equation are discussed in [3]. The purpose of this paper is to propose alternative techniques which improve the numerical reliability of existing algorithms. The proposed algorithms to solve DPLEs re present extensions of the methods for standard systems proposed by Kitagawa [6] and Barraud [5] The new approaches resemble ....

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J. Sreedhar and P. Van Dooren. Periodic Schur form and some matrix equations. In U. Helmke, R. Mennicken, and J. Saurer, editors, Proc. MTNS'93, Regensburg, Germany, volume I, pages 339--362, 1993.

....were developed to solve efficiently small order periodic Lyapunov and Sylvester equations. 1 Introduction In the last few years there has been a constantly increasing interest for the development of numerical algorithms for the analysis and design of linear periodic discrete time control systems [2, 8, 10, 12] of the form x k 1 = A k x k B k u k y k = C k x k D k u k (1) where the matrices A k 2 R n Thetan , B k 2 R n Thetam , C k 2 R p Thetan and D k 2 R p Thetam are periodic with period K 1. Of particular interest in many applications is the efficient and numerically reliable solution ....

....p Thetan and D k 2 R p Thetam are periodic with period K 1. Of particular interest in many applications is the efficient and numerically reliable solution of various types of discrete periodic Lyapunov equations (DPLEs) Several possible computational approaches to solve DPLEs are discussed in [10]. A particular family of periodic Lyapunov equations with interesting applications in balancing and model reduction are the positive discrete periodic Lyapunov equations (PDPLEs) Because the periodic solutions in this case are positive semidefinite, these equations can be solved directly for the ....

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J. Sreedhar and P. Van Dooren. Periodic Schur form and some matrix equations. In U. Helmke, R. Mennicken, and J. Saurer, editors, Proc. MTNS'93, Regensburg, Germany, volume I, pages 339--362, 1993.

....feedback and the balancing of discrete time periodic systems. In the last few years there has been a constantly increasing interest for the development of numerical algorithms for the analysis and design of linear periodic discrete time control systems (Bittanti et al. 1988, Hench and Laub 1994, Sreedhar and Van Dooren 1993). Of particular interest in the above mentioned applications is the efficient and numerically reliable solution of various types of periodic Lyapunov equations. Several possible computational approaches to solve periodic Lyapunov equation are discussed by Sreedhar and Van Dooren (1993) The ....

....Laub 1994, Sreedhar and Van Dooren 1993) Of particular interest in the above mentioned applications is the efficient and numerically reliable solution of various types of periodic Lyapunov equations. Several possible computational approaches to solve periodic Lyapunov equation are discussed by Sreedhar and Van Dooren (1993). The purpose of this paper is to propose alternative techniques which improve the numerical reliability of existing algorithms. y DLR Oberpfaffenhofen, German Aerospace Research Establishment, Institute for Robotics and System Dynamics, P.O.B. 1116, D 82230 Wessling, Germany. Tel: ....

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Sreedhar, J. and Van Dooren, P., 1993, Periodic Schur form and some matrix equations. In U. Helmke, R. Mennicken and J. Saurer (eds), Proc. MTNS'93, Regensburg, Germany, Vol. I, pp. 339--362.

....procedure would be too elaborate for our purpose here, since the precise location of closed loop poles is unimportant. Our present result is computationally cheaper too it mainly involves the solution of a discrete periodic Lyapunov equation (DPLE) for which an efficient Schur technique exists [3]. 2. Main result Theorem 1 Consider system (2) with the additional assumption that (Ak ,Bk ) is controllable, and that Ak is nonsingular. Then the periodic control law uk = GammaH k xk , Hk = I B T k P Gamma1 k Bk ) Gamma1 B T k P Gamma1 k Ak (3a) B T k (BkB T k Pk ) ....

J. Sreedhar and P. Van Dooren, "Periodic Schur form and some matrix equations," in Proc. MTNS, (Regensburg, Germany), Aug 2--6, 1993.

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J. Sreedhar and P. Van Dooren. Periodic Schur form and some matrix equations. In U. Helmke, R. Mennicken, and J. Saurer, editors, Proc. MTNS'93, Regensburg, Germany, volume I, pages 339--362, 1993.

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J. Sreedhar, P. Van Dooren, Periodic Schur form and some matrix equations, in: U. Helmke, R. Mennicken, J. Saurer (Eds.), Proc. MTNS'93, Regensburg, Germany, Academic Verlag, Berlin, vol. I, 1993, pp. 339--362.

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J. Sreedhar and P. Van Dooren. Periodic Schur form and some matrix equations. In U. Helmke, R. Mennicken, and J. Saurer, Eds., Proc. MTNS'93, Regensburg, Germany, vol. I, pp. 339--362, 1993.

No context found.

J. Sreedhar and P. Van Dooren. Periodic Schur form and some matrix equations. In U. Helmke, R. Mennicken, and J. Saurer, editors, Proc. MTNS'93, Regensburg, Germany, volume I, pages 339--362, 1993.

No context found.

J. Sreedhar and P. Van Dooren. Periodic Schur form and some matrix equations. In U. Helmke, R. Mennicken, and J. Saurer, editors, Proc. MTNS'93, Regensburg, Germany, volume I, pages 339--362, 1993.

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