algebraic_riccati_discrete.h

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 *  Copyright (c) 2020,
 *  TU Dortmund - Institute of Control Theory and Systems Engineering.
 *  All rights reserved.
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 *  Authors: Christoph Rösmann
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#ifndef SRC_NUMERICS_INCLUDE_CORBO_NUMERICS_ALGEBRAIC_RICCATI_DISCRETE_H_
#define SRC_NUMERICS_INCLUDE_CORBO_NUMERICS_ALGEBRAIC_RICCATI_DISCRETE_H_

#include <corbo-core/types.h>

#include <Eigen/Eigenvalues>

namespace corbo {

class AlgebraicRiccatiDiscrete
{
 public:
    static bool solve(const Eigen::Ref<const Eigen::MatrixXd>& A, const Eigen::Ref<const Eigen::MatrixXd>& B,
                      const Eigen::Ref<const Eigen::MatrixXd>& Q, const Eigen::Ref<const Eigen::MatrixXd>& R, Eigen::MatrixXd& X,
                      Eigen::MatrixXd* G = nullptr);

    static bool isClosedLoopStable(const Eigen::Ref<const Eigen::MatrixXd>& A, const Eigen::Ref<const Eigen::MatrixXd>& B,
                                   const Eigen::Ref<const Eigen::MatrixXd>& G);

 protected:
    static bool solveRiccatiHamiltonianSchur(const Eigen::MatrixXd& H, Eigen::MatrixXd& X);

    // Predicate for Schur block ordering (see solveRiccatiHamiltonianSchur())
    static bool isInsideUnitCircle(const Eigen::Ref<const Eigen::MatrixXd>& block) { return std::abs(block.eigenvalues()[0]) < 1; }
};

}  // namespace corbo

#endif  // SRC_NUMERICS_INCLUDE_CORBO_NUMERICS_ALGEBRAIC_RICCATI_DISCRETE_H_