The Aim Of This Work Is To Recast The H1 Loop Shaping Control Problems With Di®Erent Design Constraints In Linear Matrix Inequality (LMI) Framework. It Facilitates To Design Robust Controller In Convex Optimization Approach Which Is Computationally Superior And Easily Solvable Using Available LMI Solver. The H1 Loop Shaping Method Is A Two-Steps Design Procedure. In ¯Rst Step, The Open-Loop Singular Values Are Shaped In Order To Meet Closed-Loop Design Speci¯Cations; Whereas Second Step Is Involved With Controller Synthesis That Ensures Robustness With Respect To Unstructured Uncertainty Of The System. In The Present Work, A New Method Has Been Proposed For Pre-Compensator Selection To Shape Singular Values Of The Open-Loop Plant. Subsequently, The Condition Number Of The Pre-Compensator Is Also Minimized To Reduce Loop Deterioration And The Corresponding Problem Has Been Formulated In LMI Framework. Exploiting The H1 Loop Shaping Control Problem In Parametric Form, A General Design Framework Is Obtained. However, It Needs An Iterative Algorithm To Calculate The Robust Stability Margin. In The Present Work, The Parametric Problem Has Been Formulated In LMI Form That Circumvents Some Computational Di±Culties Of Riccati Equation Based State-Space Approach. On The Other Hand, From Implementation Point Of View, The Full-Order H1 Loop Shaping Controller Is Disadvantageous As Its Order Is High. Here, An Alternative Method Is Proposed To Design Lower-Order H1 Loop Shaping Controller In Four- Block Framework. To Show The Performance Of Lower Order Controller The Method Has Been Applied To A Physical Problem, Load Frequency Control Of Inter-Connected Power System Where Robustness Is Achieved Against Load Disturbances And Parametric Uncertainty Of The System. Further In This Work, A Local Stabilization Problem Of Uncertain LTI Plant Has Been Addressed With Bounded Control Input Constraint. It Is A Linear Case Of Actuator Satura- Tion Problem. Later, Considering Saturation Nonlinearity, Two Di®Erent Techniques Have...