On Solving Discrete-time Periodic Riccati Equations
نویسنده
چکیده
Two numerically reliable algorithms to compute the periodic nonnegative definite stabilizing solution of discrete-time periodic Riccati equations are proposed. The first method represents an extension of the periodic QZ algorithm to non-square periodic pairs, while the second method represents an extension of a quotient-product swapping and collapsing ”fast” algorithm. Both approaches are completely general being applicable to periodic Riccati equations with time varying dimensions as well as with singular control weighting. For the ”fast” method, reliable software implementation is available in a recently developed PERIODIC SYSTEMS Toolbox. Copyright c ©2005 IFAC
منابع مشابه
On solving periodic Riccati equations
Numerically reliable algorithms to compute the periodic non-negative definite stabilizing solutions of the periodic differential Riccati equation (PRDE) and discrete-time periodic Riccati equation (DPRE) are proposed. For the numerical solution of PRDEs, a new multiple shooting-type algorithm is developed to compute the periodic solutions in an arbitrary number of time moments within one period...
متن کاملMultirate Periodic Systems, o-Gap Metric and Robust Stabilization
A new discription of multirate systems, called multirate periodic system, is given using the concept of periodic time-varying input-output spaces. We then de ̄ne the o -gap metric of two multirate periodic systems and study the robust stabilization with this metric. The optimal robust stabilization margin is explicitly computed and an obsever-form suboptimal controller is given. The solution amo...
متن کاملAnalytical and Verified Numerical Results Concerning Interval Continuous-time Algebraic Riccati Equations
This paper focuses on studying the interval continuous-time algebraic Riccati equation A∗X + XA + Q − XGX = 0, both from the theoretical aspects and the computational ones. In theoretical parts, we show that Shary’s results for interval linear systems can only be partially generalized to this interval Riccati matrix equation. We then derive an efficient technique for enclosing the united stable...
متن کاملAn exponential spline for solving the fractional riccati differential equation
In this Article, proposes an approximation for the solution of the Riccati equation based on the use of exponential spline functions. Then the exponential spline equations are obtained and the differential equation of the fractional Riccati is discretized. The effect of performing this mathematical operation is obtained from an algebraic system of equations. To illustrate the benefits of the me...
متن کاملAn efficient LQR design for discrete-time linear periodic system based on a novel lifting method
This paper proposes a novel lifting method which converts the standard discrete-time linear periodic system to an augmented linear time-invariant system. The linear quadratic optimal control is then based on the solution of the discrete-time algebraic Riccati equation associated with the augmented linear time-invariant model. An efficient algorithm for solving the Riccati equation is derived by...
متن کامل