## Uncertainty-averaging approach to output feedback optimal guaranteed cost control of uncertain systems.(English)Zbl 0853.93065

The authors are well known experts on control theory of systems with uncertainties. In the article under review they introduce a new class of systems with a structural uncertainty. The systems are linear, modelled by the equations: \begin{aligned} \dot x(t) & = A(t) x(t) + B(t) u(t) + C_s (t) \xi (t), \\ \dot y(t) & = H(t) x(t) + \sum^k_{s = 1} V_s \xi_s (t), \\ \dot z_i (t) & = K_i (t) x(t) + G_i (t) u(t),\;i = 1, 2, \dots, k, \end{aligned} where $$x \in \mathbb{R}^n$$ is the state, $$u \in \mathbb{R}^m$$ is the control, $$y \in \mathbb{R}^t$$ is the observation, $$\xi$$ is the uncertainty input vector, $$z$$ the uncertainty output, while all capital letters denote appropriate matrices, whose entries are functions bounded and piecewise continuous on $$[0,T]$$. The relation between the uncertainty input and control is given in vector form: $$\xi (t) = \Phi (t,x (.) |^t_0$$, $${\mathbf u} (.) |^t_0)$$.
Structural uncertainties are introduced, obeying an averaged integral quadratic constraint. This system is reduced to a pair of parametrized Riccati equations. The authors construct a controller, and prove that this controller satisfies the required bounds, and is a guaranteed cost controller. The authors follow the general ideas of the $$S$$-procedure discussed by A. M. Megretsky and S. Treil in [J. Math. Syst. Estim. Control 3, 301-319 (1993; Zbl 0781.93079)], but with differential initial conditions. They show that their system is more general, and that the results of Megretsky and Treil may be easily obtained after a minor modification of their system.
Reviewer: V.Komkov (Roswell)

### MSC:

 93C41 Control/observation systems with incomplete information 49N10 Linear-quadratic optimal control problems 93B52 Feedback control

Zbl 0781.93079
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### References:

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