S. BOYD, V. BALAKRISHNAN, E. FERON, and L. El GHAOUI. Control system analysis and synthesis via linear matrix inequalities. Proc. ACC, pages 2147--2154, 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....to the state space nonlinear H1 control problem, and characterize the solutions in terms of convex conditions instead of the Hamilton Jacobi equations or inequalities. This is motivated by the fact that, essentially, the linear H1 control problem can be characterized as a convex problem [23, 3]. We examine the convexity of the nonlinear H1 control problem, and deal with a class of nonlinear H1 control problem whose solvability Electrical Engineering 116 81, California Institute of Technology, Pasadena, CA 91125. 1 conditions are convexly characterized as some algebraic nonlinear ....

.... as some algebraic nonlinear matrix inequalities (NLMIs) This makes the computation very appealing, since the solutions to this class of nonlinear H1 problems are based on the required solutions to the corresponding algebraic NLMIs, which can be solved via the convex optimization methods[3]. The analogical treatments in linear case, which are characterized in terms of linear matrix inequalities (LMIs) can be found in [20, 22, 18, 24, 9, 15] The other features of the suggested approach are that the nonlinear system considered has few structural constraints; the system coefficient ....

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Boyd, S.P. (1993), Control Systems Analysis and Synthesis via Linear Matrix Inequalities, 1993 ACC (Plenary Lecture), San Francisco, CA. pp.2147 -- 2154.

.... have an old history dating back more than 100 years to Lyapunov s theory for stability of differential equations, e.g. 72, 61] They were studied and applied in engineering applications as early as the 1960s, e.g. 101, 100] and continued into the 1980 s (see e.g. the historical outline in [18]) In addition, SDP is a special case of optimization over cone constraints (generalized linear programming) which dates back more than 30 years to e.g. Bellman and Fan [10] and was an ongoing active area of research, e.g. 11, 33, 21, 22, 47, 108, 69, 17] The last ten years has seen an ....

S. BOYD, V. BALAKRISHNAN, E. FERON, and L. El GHAOUI. Control system analysis and synthesis via linear matrix inequalities. Proc. ACC, pages 2147--2154, 1993.

....but is true when the trace is a constant function on the feasible set, see e.g. 26] This can be used to exploit structure and solve large scale problems. For more on eigenvalue optimization, see [37] 4. 3 Engineering Many early applications of SDP appeared in the Engineering literature, e.g. [11, 66, 65]. This was particularly evident in control theory, where it has emerged as an important practical tool for the analysis of nonlinear and time varying systems, and for controller synthesis. This is of great interest to computeraided control system design. SDPs also arise in other fields of ....

....of nonlinear and time varying systems, and for controller synthesis. This is of great interest to computeraided control system design. SDPs also arise in other fields of engineering and mathematics, such as structural optimization, circuit design, signal processing, and statistics, see e.g. [11, 62, 63, 17, 18, 50, 56]. For other applications include solving Ricatti equations, see e.g. 13, 64] In this arena SDP is usually known as LMI: Linear Matrix Inequalities. A typical example of an SDP application in Systems and Control is the numerical search for Lyapunov inequalities and also for Lyapunov functions ....

S. BOYD, V. BALAKRISHNAN, E. FERON, and L. El GHAOUI. Control system analysis and synthesis via linear matrix inequalities. Proc. ACC, pages 2147--2154, 1993.

....at the University of New Mexico. 2 Ph.D. Student, luke eece.unm.edu, http: www.eece.unm.edu students luke 3 Professor 4 Associate Professor The papers discussed in this survey consider both the single input case (q = 1 in [1] 14] 18] and [19] and the multiple input case (q 1 in [6] and [9] In the former, the state control vector is k T = k 1 ; k 2 ; k n ] and in the latter, the control matrix is a q Theta n array. Blondel [5] demonstrates that it is not possible to rationally decide 5 whether or not a set of three or more systems is simultaneously ....

....Ackermann [1] considers a space K containing all linear state feedback control gain vectors k. He then partitions K to obtain a subspace guaranteed to simultaneously stabilize systems. Howitt and Luus [14] give a nonlinear programming problem which produces the linear controller. Boyd, et al. [6] show that simultaneous stabilizability can be guaranteed if there exists a single solution to a set of m linear matrix inequalities. Paskota, et al. 18] simultaneously stabilize systems by solving nonlinear Li enard Chipart constraints. Dorato, et al. 10] apply a relatively new computational ....

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S. Boyd, V. Balakrishnan, E. Feron, and L. El Ghaoui. Control System Analysis and Synthesis via Linear Matrix Inequalities. In Proceedings of the 1993 American Control Conference, pages 2147--2154, San Francisco, California, June 1993.

....see e.g. 24, 1] Another reason for the interest is that SDPs can be solved efficiently using interior point methods. More applications and evidence of the current high level of activity can be found in the recent theses: 2, 43, 22, 39, 25, 65, 28, 26, 54] and in the recent books and notes [63, 9, 36, 61, 56, 48, 38]. SDP has many similarities with LP. One important point, mentioned above, is that SDP problems can be solved very efficiently using primal dual interior point (p d i p) methods. These methods are based on applying Newton s method to the Karush Kuhn Tucker (KKT) optimality conditions: dual ....

S. BOYD, V. BALAKRISHNAN, E. FERON, and L. El GHAOUI. Control system analysis and synthesis via linear matrix inequalities. Proc. ACC, pages 2147--2154, 1993.

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S. BOYD, V. BALAKRISHNAN, E. FERON, and L. El GHAOUI. Control system analysis and synthesis via linear matrix inequalities. Proc. ACC, pages 2147--2154, 1993.

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