On a quadratic matrix inequality and the corresponding algebraic Riccati equation†

Badawi, Faris A.

doi:10.1080/00207178208932895

Cited by 12 publications

(2 citation statements)

References 3 publications

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“…We can express the Bellman inequalities (8) as for all z ∈ R n , where we define This is equivalent to the condition, for t = 0, …, N −1, which can be written as Each of the terms , , , , , in the block matrix inequalities are linear functions of the variables Q t , q t , s t , P t , p t , c t , S t , R t , and r t . Thus, inequalities (11) are linear matrix inequalities (LMIs) 40–46. In particular, the set of matrices Q t , q t , s t , P t , p t , c t , S t , R t , and r t that satisfy (11) is convex.…”

Section: Finite Horizonmentioning

confidence: 99%

Synthesis of Aryl‐Substituted Naphthalene‐Linked Pyrrolobenzodiazepine Conjugates as Potential Anticancer Agents with Apoptosis‐Inducing Ability

et al. 2011

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A library of new aryl-substituted naphthalene C8-linked pyrrolo[2,1-c][1,4]benzodiazepine (PBD) conjugates with various linker architectures were designed, synthesized, and evaluated for their anticancer activity against a panel of 11 human cancer cell lines. All 32 conjugates show anticancer potential, with some of them exhibiting particularly high activity (0.01-0.19 μM). Thermal denaturation studies showed effective DNA binding capacity relative to DC-81. In assays for biological activity relating to cell-cycle distribution, these PBD conjugates induce G₀/G₁-phase arrest and also cause an increase in the levels of p53 and caspase-9 proteins, followed by apoptotic cell death. One conjugate in particular is the most promising candidate of the series, with the potential to be selected for further studies, either alone or in combination with existing anticancer therapies.

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Section: Finite Horizonmentioning

confidence: 99%

Synthesis of Aryl‐Substituted Naphthalene‐Linked Pyrrolobenzodiazepine Conjugates as Potential Anticancer Agents with Apoptosis‐Inducing Ability

et al. 2011

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“…with variable P. The optimal point is P = P , and the optimal value of this problem is J [8,1,20,3,7,29]. For future use we make some important comments about this problem.…”

Section: Linear Quadratic Controlmentioning

confidence: 99%

Performance bounds for linear stochastic control

Yang

Boyd

2009

Systems & Control Letters

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a b s t r a c tWe develop computational bounds on performance for causal state feedback stochastic control with linear dynamics, arbitrary noise distribution, and arbitrary input constraint set. This can be very useful as a comparison with the performance of suboptimal control policies, which we can evaluate using Monte Carlo simulation. Our method involves solving a semidefinite program (a linear optimization problem with linear matrix inequality constraints), a convex optimization problem which can be efficiently solved. Numerical experiments show that the lower bound obtained by our method is often close to the performance achieved by several widely-used suboptimal control policies, which shows that both are nearly optimal. As a by-product, our performance bound yields approximate value functions that can be used as control Lyapunov functions for suboptimal control policies.

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Fixed-structure robust controller synthesis via decentralized static output feedback

Erwin

Sparks

Bernstein

1998

Int. J. Robust Nonlinear Control

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This paper describes and illustrates a unified methodology for robust, fixed‐structure controller synthesis. The approach is based upon direct fixed‐structure controller synthesis using a decentralized static output feedback formulation as a general framework for representing a large class of controller structures. Scaled Popov bounds for the real structured singular value are used to account for real parameter uncertainty and provide the means for optimizing a worst‐case ℋ︁2 cost bound with respect to the free parameters of the controller. Quasi‐Newton optimization algorithms are used to solve the resulting numerical optimization problem. Initial stability multiplier and scaling matrices needed in scaled Popov synthesis are obtained by solving an LMI feasibility problem. Using both centralized and decentralized controller structures, numerical results are obtained for a 16th‐order acoustic duct model with uncertain damped natural frequencies and for a two‐dimensional beam‐spring model with uncertain actuator locations. © 1998 John Wiley & Sons, Ltd.

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On a quadratic matrix inequality and the corresponding algebraic Riccati equation†

Cited by 12 publications

References 3 publications

Synthesis of Aryl‐Substituted Naphthalene‐Linked Pyrrolobenzodiazepine Conjugates as Potential Anticancer Agents with Apoptosis‐Inducing Ability

Synthesis of Aryl‐Substituted Naphthalene‐Linked Pyrrolobenzodiazepine Conjugates as Potential Anticancer Agents with Apoptosis‐Inducing Ability

Performance bounds for linear stochastic control

Fixed-structure robust controller synthesis via decentralized static output feedback

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